Finite Group Databasebeta

← C109×#16535 #42134529

Subgroups — C109×#16535 #42134529

Order 27904.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C109C211yesmaximal, characteristic, complemented
2C2×#394×C109C211yesmaximal, characteristic, complemented
3C2×#392×C109C211yesmaximal, characteristic
4C2×#388×C109C211yesmaximal, characteristic, complemented
5C109×#1443C211yesmaximal, characteristic, complemented
6C109×#1442C211yesmaximal, characteristic, complemented
7C109×#1439C211yesmaximal, characteristic, complemented
8C109×#1439C211yesmaximal, characteristic, complemented
9C109×#1438C211yesmaximal, characteristic, complemented
10C109×#1438C211yesmaximal, characteristic, complemented
11C109×#1438C211yesmaximal, characteristic, complemented
12C109×#1438C211yesmaximal, characteristic, complemented
13C109×#1438C211yesmaximal, characteristic, complemented
14C109×#1437C211yesmaximal, characteristic, complemented
15C109×#1437C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C22×C4⋊C4×C109C2211yescharacteristic
20C22×C4⋊C4×C109C2211yescharacteristic
21C22×C22⋊C4×C109C2211yescharacteristic
22C22×C22⋊C4×C109C2211yescharacteristic
23C22×C22⋊C4×C109C2211yescharacteristic
24C22×C22⋊C4×C109C2211yescharacteristic
25C22×C22⋊C4×C109C2211yescharacteristic
26C22×C22⋊C4×C109C2211yescharacteristic
27C22×C22⋊C4×C109C2211yescharacteristic
28C22×C22⋊C4×C109C2211yescharacteristic
29C22×C22⋊C4×C109C2211yescharacteristic
30C22×C22⋊C4×C109C2211yescharacteristic
31C22×C22⋊C4×C109C2211yescharacteristic
32C22×C22⋊C4×C109C2211yescharacteristic
33C22×C22⋊C4×C109C2211yescharacteristic
34C22×C22⋊C4×C109C2211yescharacteristic
35C22×C22⋊C4×C109C2211yescharacteristic
36C22×C42×C109C2211yescharacteristic
37#397×C109—24no—
38#394×C109—24no—
39#392×C109—24no—
40#388×C109—24no—
41C2×#95×C109C2211yescharacteristic
42C2×#95×C109C2211yescharacteristic
43C2×#95×C109C2211yescharacteristic
44C2×#95×C109C2211yescharacteristic
45C2×#95×C109C2211yescharacteristic
46C2×#95×C109C2211yescharacteristic
47C2×#95×C109C2211yescharacteristic
48C2×#95×C109C2211yescharacteristic
49C2×#95×C109C2211yescharacteristic
50C2×#95×C109C2211yescharacteristic
51C2×#95×C109C2211yescharacteristic
52C2×#95×C109C2211yescharacteristic
53C2×#95×C109C2211yescharacteristic
54C2×#95×C109C2211yescharacteristic
55C25×C109C2311yescharacteristic
56C25×C109C2311yescharacteristic
57C25×C109C2311yescharacteristic
58C22×D4×C109—22no—
59C22×D4×C109—22no—
60C22×D4×C109—22no—
61C22×D4×C109—22no—
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—41no—
68C22×D4×C109—41no—
69C22×D4×C109—41no—
70C22×D4×C109—41no—
71C22×D4×C109—41no—
72C22×D4×C109—41no—
73C22×D4×C109—41no—
74C22×D4×C109—41no—
75C22×D4×C109—41no—
76C22×D4×C109—41no—
77C22×D4×C109—41no—
78C22×D4×C109—41no—
79C23×C4×C109C2311yescharacteristic
80C23×C4×C109C2311yescharacteristic
81C23×C4×C109C2311yescharacteristic
82C23×C4×C109C2311yescharacteristic
83C23×C4×C109C2311yescharacteristic
84C23×C4×C109C2311yescharacteristic
85C23×C4×C109C2311yescharacteristic
86C23×C4×C109C2311yescharacteristic
87C23×C4×C109C2311yescharacteristic
88C23×C4×C109C2311yescharacteristic
89C23×C4×C109C2311yescharacteristic
90C23×C4×C109C2311yescharacteristic
91C2×C4⋊C4×C109—22no—
92C2×C4⋊C4×C109—22no—
93C2×C4⋊C4×C109—22no—
94C2×C4⋊C4×C109—41no—
95C2×C4⋊C4×C109—41no—
96C2×C4⋊C4×C109—41no—
97C2×C22⋊C4×C109—22no—
98C2×C22⋊C4×C109—22no—
99C2×C22⋊C4×C109—22no—
100C2×C22⋊C4×C109—22no—
101C2×C22⋊C4×C109—22no—
102C2×C22⋊C4×C109—22no—
103C2×C22⋊C4×C109—22no—
104C2×C22⋊C4×C109—22no—
105C2×C22⋊C4×C109—22no—
106C2×C22⋊C4×C109—22no—
107C2×C22⋊C4×C109—22no—
108C2×C22⋊C4×C109—22no—
109C2×C22⋊C4×C109—22no—
110C2×C22⋊C4×C109—22no—
111C2×C22⋊C4×C109—22no—
112C2×C22⋊C4×C109—22no—
113C2×C22⋊C4×C109—22no—
114C2×C22⋊C4×C109—22no—
115C2×C22⋊C4×C109—22no—
116C2×C22⋊C4×C109—22no—
117C2×C22⋊C4×C109—41no—
118C2×C22⋊C4×C109—41no—
119C2×C22⋊C4×C109—41no—
120C2×C22⋊C4×C109—41no—
121C2×C22⋊C4×C109—41no—
122C2×C22⋊C4×C109—41no—
123C2×C22⋊C4×C109—41no—
124C2×C22⋊C4×C109—41no—
125C2×C22⋊C4×C109—41no—
126C2×C22⋊C4×C109—41no—
127C2×C22⋊C4×C109—41no—
128C2×C22⋊C4×C109—41no—
129C2×C22⋊C4×C109—41no—
130C2×C22⋊C4×C109—41no—
131C2×C22⋊C4×C109—41no—
132C2×C22⋊C4×C109—41no—
133C2×C22⋊C4×C109—41no—
134C2×C22⋊C4×C109—41no—
135C2×C22⋊C4×C109—41no—
136C2×C22⋊C4×C109—41no—
137C2×C22⋊C4×C109—41no—
138C2×C22⋊C4×C109—41no—
139C2×C22⋊C4×C109—41no—
140C2×C22⋊C4×C109—41no—
141C2×C22⋊C4×C109D414yes—
142C2×C42×C109—22no—
143C2×C42×C109—41no—
144C2×C42×C109—41no—
145#95×C109—22no—
146#95×C109—22no—
147#95×C109—22no—
148#95×C109—22no—
149#95×C109—22no—
150#95×C109—22no—
151#95×C109—41no—
152#95×C109—41no—
153#95×C109—41no—
154#95×C109—41no—
155#95×C109—41no—
156#95×C109—41no—
157#95×C109—41no—
158#95×C109D414yescomplemented
159C24×C109—21no—
160C24×C109—21no—
161C24×C109—21no—
162C24×C109—21no—
163C24×C109—21no—
164C24×C109—21no—
165C24×C109—21no—
166C24×C109—21no—
167C24×C109—21no—
168C24×C109—21no—
169C24×C109—21no—
170C24×C109—21no—
171C24×C109—21no—
172C24×C109—21no—
173C24×C109—21no—
174C24×C109—21no—
175C24×C109—21no—
176C24×C109—21no—
177C24×C109—21no—
178C24×C109—21no—
179C24×C109—21no—
180C24×C109—21no—
181C24×C109—21no—
182C24×C109—21no—
183C24×C109—21no—
184C24×C109—21no—
185C24×C109—21no—
186C24×C109—21no—
187C24×C109—21no—
188C24×C109—21no—
189C24×C109—21no—
190C24×C109—21no—
191C24×C109—21no—
192C24×C109—21no—
193C24×C109—21no—
194C24×C109—21no—
195C24×C109—21no—
196C24×C109—21no—
197C24×C109—21no—
198C24×C109—21no—
199C24×C109—21no—
200C24×C109—21no—
201C24×C109C2×D412yes—
202C24×C109#4112yes—
203C24×C109#4112yes—
204C24×C109C2411yescharacteristic
205C2×D4×C109—44no—
206C2×D4×C109—44no—
207C2×D4×C109—44no—
208C2×D4×C109—44no—
209C2×D4×C109—44no—
210C2×D4×C109—44no—
211C2×D4×C109—44no—
212C2×D4×C109—44no—
213C2×D4×C109—44no—
214C2×D4×C109—44no—
215C2×D4×C109—44no—
216C2×D4×C109—44no—
217C2×D4×C109—44no—
218C2×D4×C109—44no—
219C2×D4×C109—44no—
220C2×D4×C109—44no—
221C2×D4×C109—44no—
222C2×D4×C109—44no—
223C2×D4×C109—44no—
224C2×D4×C109—44no—
225C2×D4×C109—44no—
226C22×C4×C109—21no—
227C22×C4×C109—21no—
228C22×C4×C109—21no—
229C22×C4×C109—21no—
230C22×C4×C109—21no—
231C22×C4×C109—21no—
232C22×C4×C109—21no—
233C22×C4×C109—21no—
234C22×C4×C109—21no—
235C22×C4×C109—21no—
236C22×C4×C109—21no—
237C22×C4×C109—21no—
238C22×C4×C109—21no—
239C22×C4×C109—21no—
240C22×C4×C109—21no—
241C22×C4×C109—21no—
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—21no—
245C22×C4×C109—21no—
246C22×C4×C109—21no—
247C22×C4×C109—21no—
248C22×C4×C109—21no—
249C22×C4×C109—21no—
250C22×C4×C109—21no—
251C22×C4×C109—21no—
252C22×C4×C109—21no—
253C22×C4×C109—21no—
254C22×C4×C109—21no—
255C22×C4×C109—21no—
256C22×C4×C109—21no—
257C22×C4×C109—21no—
258C22×C4×C109—21no—
259C22×C4×C109—21no—
260C22×C4×C109—21no—
261C22×C4×C109—21no—
262C22×C4×C109—21no—
263C22×C4×C109—21no—
264C22×C4×C109—21no—
265C22×C4×C109—21no—
266C22×C4×C109—21no—
267C22×C4×C109—21no—
268C22×C4×C109—21no—
269C22×C4×C109—21no—
270C22×C4×C109—21no—
271C22×C4×C109—21no—
272C22×C4×C109—21no—
273C22×C4×C109—21no—
274C22×C4×C109—21no—
275C22×C4×C109—21no—
276C22×C4×C109—21no—
277C22×C4×C109—21no—
278C22×C4×C109—21no—
279C22×C4×C109—21no—
280C22×C4×C109—21no—
281C22×C4×C109—21no—
282C22×C4×C109—21no—
283C22×C4×C109—21no—
284C22×C4×C109—21no—
285C22×C4×C109—21no—
286C22×C4×C109—21no—
287C22×C4×C109—21no—
288C22×C4×C109—21no—
289C22×C4×C109—21no—
290C22×C4×C109—21no—
291C22×C4×C109—21no—
292C22×C4×C109—21no—
293C22×C4×C109—21no—
294C22×C4×C109—21no—
295C22×C4×C109—21no—
296C22×C4×C109—21no—
297C22×C4×C109—21no—
298C22×C4×C109—21no—
299C22×C4×C109—21no—
300C22×C4×C109—21no—
301C22×C4×C109—21no—
302C22×C4×C109C2×D412yes—
303C22×C4×C109C2×D412yes—
304C22×C4×C109C2×D412yes—
305C22×C4×C109C2×D412yes—
306C22×C4×C109C2×D412yes—
307C22×C4×C109#4112yes—
308C22×C4×C109#4112yes—
309C22×C4×C109#4112yes—
310C4⋊C4×C109—44no—
311C4⋊C4×C109—44no—
312C22⋊C4×C109—28no—
313C22⋊C4×C109—44no—
314C22⋊C4×C109—44no—
315C22⋊C4×C109—44no—
316C22⋊C4×C109—44no—
317C22⋊C4×C109—44no—
318C22⋊C4×C109—44no—
319C22⋊C4×C109—44no—
320C22⋊C4×C109—44no—
321C22⋊C4×C109—44no—
322C22⋊C4×C109—44no—
323C22⋊C4×C109—44no—
324C22⋊C4×C109—44no—
325C22⋊C4×C109—44no—
326C22⋊C4×C109—44no—
327C42×C109—44no—
328C23×C109—22no—
329C23×C109—22no—
330C23×C109—22no—
331C23×C109—22no—
332C23×C109—22no—
333C23×C109—22no—
334C23×C109—22no—
335C23×C109—22no—
336C23×C109—22no—
337C23×C109—22no—
338C23×C109—22no—
339C23×C109—22no—
340C23×C109—22no—
341C23×C109—22no—
342C23×C109—22no—
343C23×C109—22no—
344C23×C109—22no—
345C23×C109—22no—
346C23×C109—22no—
347C23×C109—22no—
348C23×C109—22no—
349C23×C109—41no—
350C23×C109—41no—
351C23×C109—41no—
352C23×C109—41no—
353C23×C109—41no—
354C23×C109—41no—
355C23×C109—41no—
356C23×C109—41no—
357C23×C109—41no—
358C23×C109—41no—
359C23×C109—41no—
360C23×C109—41no—
361C23×C109—41no—
362C23×C109—41no—
363C23×C109—41no—
364C23×C109—41no—
365C23×C109—41no—
366C23×C109—41no—
367C23×C109—41no—
368C23×C109—41no—
369C23×C109—41no—
370C23×C109—41no—
371C23×C109—41no—
372C23×C109—41no—
373C23×C109—41no—
374C23×C109—41no—
375C23×C109—41no—
376C23×C109—41no—
377C23×C109—41no—
378C23×C109—41no—
379C23×C109—41no—
380C23×C109—41no—
381C23×C109—41no—
382C23×C109—41no—
383C23×C109—41no—
384C23×C109—41no—
385C23×C109—41no—
386C23×C109—41no—
387C23×C109—41no—
388C23×C109—41no—
389C23×C109—41no—
390C23×C109—41no—
391C23×C109—41no—
392C23×C109—41no—
393C23×C109—41no—
394C23×C109—41no—
395C23×C109—41no—
396C23×C109—41no—
397C23×C109—41no—
398C23×C109—41no—
399C23×C109—41no—
400C23×C109—41no—
401C23×C109—41no—
402C23×C109—41no—
403C23×C109—41no—
404C23×C109—41no—
405C23×C109—41no—
406C23×C109—41no—
407C23×C109—41no—
408C23×C109—41no—
409C23×C109—41no—
410C23×C109—41no—
411C23×C109—41no—
412C23×C109—41no—
413C23×C109—41no—
414C23×C109—41no—
415C23×C109—41no—
416C23×C109—41no—
417C23×C109—41no—
418C23×C109—41no—
419C23×C109—41no—
420C23×C109—41no—
421C23×C109—41no—
422C23×C109—41no—
423C23×C109—41no—
424C23×C109—41no—
425C23×C109—41no—
426C23×C109—41no—
427C23×C109—41no—
428C23×C109—41no—
429C23×C109—41no—
430C23×C109—41no—
431C23×C109—41no—
432C23×C109—41no—
433C23×C109C22×D411yescharacteristic
434C23×C109C22×D411yescharacteristic
435C23×C109C2×#4111yescharacteristic
436C23×C109C2×#4111yescharacteristic
437C23×C109C2×#4111yescharacteristic
438C23×C109C2×#4111yescharacteristic
439C23×C109C2×#4111yescharacteristic
440C23×C109H(5,𝔽2)11yescharacteristic
441C23×C109H(5,𝔽2)11yescharacteristic
442C23×C109H(5,𝔽2)11yescharacteristic
443C23×C109H(5,𝔽2)11yescharacteristic
444C23×C109H(5,𝔽2)11yescharacteristic
445C23×C109H(5,𝔽2)11yescharacteristic
446C23×C109H(5,𝔽2)11yescharacteristic
447C23×C109H(5,𝔽2)11yescharacteristic
448D4×C109—416no—
449D4×C109—416no—
450D4×C109—416no—
451C2×C4×C109—22no—
452C2×C4×C109—22no—
453C2×C4×C109—22no—
454C2×C4×C109—22no—
455C2×C4×C109—22no—
456C2×C4×C109—22no—
457C2×C4×C109—22no—
458C2×C4×C109—22no—
459C2×C4×C109—22no—
460C2×C4×C109—22no—
461C2×C4×C109—22no—
462C2×C4×C109—22no—
463C2×C4×C109—22no—
464C2×C4×C109—22no—
465C2×C4×C109—22no—
466C2×C4×C109—22no—
467C2×C4×C109—22no—
468C2×C4×C109—22no—
469C2×C4×C109—22no—
470C2×C4×C109—22no—
471C2×C4×C109—22no—
472C2×C4×C109—22no—
473C2×C4×C109—22no—
474C2×C4×C109—22no—
475C2×C4×C109—41no—
476C2×C4×C109—41no—
477C2×C4×C109—41no—
478C2×C4×C109—41no—
479C2×C4×C109—41no—
480C2×C4×C109—41no—
481C2×C4×C109—41no—
482C2×C4×C109—41no—
483C2×C4×C109—41no—
484C2×C4×C109—41no—
485C2×C4×C109—41no—
486C2×C4×C109—41no—
487C2×C4×C109—41no—
488C2×C4×C109—41no—
489C2×C4×C109—41no—
490C2×C4×C109—41no—
491C2×C4×C109—41no—
492C2×C4×C109—41no—
493C2×C4×C109—41no—
494C2×C4×C109—41no—
495C2×C4×C109—41no—
496C2×C4×C109—41no—
497C2×C4×C109—41no—
498C2×C4×C109—41no—
499C2×C4×C109—41no—
500C2×C4×C109—41no—
501C2×C4×C109—41no—
502C2×C4×C109—41no—
503C2×C4×C109—41no—
504C2×C4×C109—41no—
505C2×C4×C109—41no—
506C2×C4×C109—41no—
507C2×C4×C109—41no—
508C2×C4×C109—41no—
509C2×C4×C109—41no—
510C2×C4×C109—41no—
511C2×C4×C109—41no—
512C2×C4×C109—41no—
513C2×C4×C109—41no—
514C2×C4×C109—41no—
515C2×C4×C109—41no—
516C2×C4×C109—41no—
517C2×C4×C109—41no—
518C2×C4×C109—41no—
519C2×C4×C109—41no—
520C2×C4×C109—41no—
521C2×C4×C109—41no—
522C2×C4×C109—41no—
523C2×C4×C109—41no—
524C2×C4×C109—41no—
525C2×C4×C109—41no—
526C2×C4×C109—41no—
527C2×C4×C109—41no—
528C2×C4×C109—41no—
529C2×C4×C109—41no—
530C2×C4×C109—41no—
531C2×C4×C109—41no—
532C2×C4×C109—41no—
533C2×C4×C109—41no—
534C2×C4×C109—41no—
535C22×C109—42no—
536C22×C109—42no—
537C22×C109—42no—
538C22×C109—42no—
539C22×C109—42no—
540C22×C109—42no—
541C22×C109—42no—
542C22×C109—42no—
543C22×C109—42no—
544C22×C109—42no—
545C22×C109—42no—
546C22×C109—42no—
547C22×C109—42no—
548C22×C109—42no—
549C22×C109—42no—
550C22×C109—42no—
551C22×C109—42no—
552C22×C109—42no—
553C22×C109—42no—
554C22×C109—42no—
555C22×C109—42no—
556C22×C109—81no—
557C22×C109—81no—
558C22×C109—81no—
559C22×C109—81no—
560C22×C109—81no—
561C22×C109—81no—
562C22×C109—81no—
563C22×C109—81no—
564C22×C109—81no—
565C22×C109—81no—
566C22×C109—81no—
567C22×C109—81no—
568C22×C109—81no—
569C22×C109—81no—
570C22×C109—81no—
571C22×C109—81no—
572C22×C109—81no—
573C22×C109—81no—
574C22×C109—81no—
575C22×C109—81no—
576C22×C109—81no—
577C22×C109—81no—
578C22×C109—81no—
579C22×C109—81no—
580C22×C109#52511yescharacteristic
581C22×C109#52911yescharacteristic
582C22×C109#53211yescharacteristic
583C22×C109#53411yescharacteristic
584C22×C109#53511yescharacteristic
585C22×C109#53511yescharacteristic
586C22×C109#53511yescharacteristic
587C22×C109#53811yescharacteristic
588C22×C109#53811yescharacteristic
589C22×C109#53811yescharacteristic
590C22×C109#53811yescharacteristic
591C22×C109#53811yescharacteristic
592C22×C109#53811yescharacteristic
593C22×C109#53811yescharacteristic
594C22×C109#53811yescharacteristic
595C22×C109#54011yescharacteristic
596C22×C109#54011yescharacteristic
597C22×C109#54011yescharacteristic
598C22×C109#54011yescharacteristic
599C22×C109D4211yescharacteristic
600C22×C109#54611yescharacteristic
601C22×C109#54611yescharacteristic
602C22×C109#54611yescharacteristic
603C22×C109#54611yescharacteristic
604C22×C109#54611yescharacteristic
605C22×C109#55011yescharacteristic
606C22×C109#55111yescharacteristic
607C22×C109#55111yescharacteristic
608C22×C109#55311yescharacteristic
609C22×C109#55311yescharacteristic
610C22×C109#55311yescharacteristic
611C22×C109#56011yescharacteristic
612C22×C109#56011yescharacteristic
613C22×C109#56011yescharacteristic
614C22×C109H(3,𝔽4)11yescharacteristic
615C4×C109—42no—
616C4×C109—42no—
617C4×C109—42no—
618C4×C109—42no—
619C4×C109—42no—
620C4×C109—42no—
621C4×C109—42no—
622C4×C109—42no—
623C4×C109—81no—
624C4×C109—81no—
625C4×C109—81no—
626C4×C109—81no—
627#16535C10911yesmaximal, characteristic, direct product factor, Sylow
628C2×C109—82no—
629C2×C109—82no—
630C2×C109—82no—
631C2×C109#246411yescharacteristic
632C2×C109#247111yescharacteristic
633C2×C109#255911yescharacteristic
634C2×C109#263111yescharacteristic
635C2×C109#264811yescharacteristic
636C2×C109#266111yescharacteristic
637C2×C109#267011yescharacteristic
638C2×C109#267311yescharacteristic
639C2×C109#268511yescharacteristic
640C2×C109#269711yescharacteristic
641C2×C109#270311yescharacteristic
642C2×C109#271411yescharacteristic
643C2×C109#275311yescharacteristic
644C2×C109#277811yescharacteristic
645C2×C109#282811yescharacteristic
646C2×#397C2×C10911yescharacteristic, complemented
647C2×#394C2×C10911yescharacteristic, complemented
648C2×#392C2×C10911yescharacteristic
649C2×#388C2×C10911yescharacteristic, complemented
650#1443C2×C10911yescharacteristic, complemented
651#1442C2×C10911yescharacteristic, complemented
652#1439C2×C10911yescharacteristic, complemented
653#1439C2×C10911yescharacteristic, complemented
654#1438C2×C10911yescharacteristic, complemented
655#1438C2×C10911yescharacteristic, complemented
656#1438C2×C10911yescharacteristic, complemented
657#1438C2×C10911yescharacteristic, complemented
658#1438C2×C10911yescharacteristic, complemented
659#1437C2×C10911yescharacteristic, complemented
660#1437C2×C10911yescharacteristic, complemented
661C109#1653511yescharacteristic, direct product factor, Sylow
662C23×D4C22×C10911yescharacteristic
663C23×D4C22×C10911yescharacteristic
664C23×D4C22×C10911yescharacteristic
665C22×C4⋊C4C22×C10911yescharacteristic
666C22×C4⋊C4C22×C10911yescharacteristic
667C22×C22⋊C4C22×C10911yescharacteristic
668C22×C22⋊C4C22×C10911yescharacteristic
669C22×C22⋊C4C22×C10911yescharacteristic
670C22×C22⋊C4C22×C10911yescharacteristic
671C22×C22⋊C4C22×C10911yescharacteristic
672C22×C22⋊C4C22×C10911yescharacteristic
673C22×C22⋊C4C22×C10911yescharacteristic
674C22×C22⋊C4C22×C10911yescharacteristic
675C22×C22⋊C4C22×C10911yescharacteristic
676C22×C22⋊C4C22×C10911yescharacteristic
677C22×C22⋊C4C22×C10911yescharacteristic
678C22×C22⋊C4C22×C10911yescharacteristic
679C22×C22⋊C4C22×C10911yescharacteristic
680C22×C22⋊C4C22×C10911yescharacteristic
681C22×C22⋊C4C22×C10911yescharacteristic
682C22×C42C22×C10911yescharacteristic
683#397—24no—
684#394—24no—
685#392—24no—
686#388—24no—
687C2×#95C22×C10911yescharacteristic
688C2×#95C22×C10911yescharacteristic
689C2×#95C22×C10911yescharacteristic
690C2×#95C22×C10911yescharacteristic
691C2×#95C22×C10911yescharacteristic
692C2×#95C22×C10911yescharacteristic
693C2×#95C22×C10911yescharacteristic
694C2×#95C22×C10911yescharacteristic
695C2×#95C22×C10911yescharacteristic
696C2×#95C22×C10911yescharacteristic
697C2×#95C22×C10911yescharacteristic
698C2×#95C22×C10911yescharacteristic
699C2×#95C22×C10911yescharacteristic
700C2×#95C22×C10911yescharacteristic
701C25C23×C10911yescharacteristic
702C25C23×C10911yescharacteristic
703C25C23×C10911yescharacteristic
704C22×D4—22no—
705C22×D4—22no—
706C22×D4—22no—
707C22×D4—22no—
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C23×C4C23×C10911yescharacteristic
726C23×C4C23×C10911yescharacteristic
727C23×C4C23×C10911yescharacteristic
728C23×C4C23×C10911yescharacteristic
729C23×C4C23×C10911yescharacteristic
730C23×C4C23×C10911yescharacteristic
731C23×C4C23×C10911yescharacteristic
732C23×C4C23×C10911yescharacteristic
733C23×C4C23×C10911yescharacteristic
734C23×C4C23×C10911yescharacteristic
735C23×C4C23×C10911yescharacteristic
736C23×C4C23×C10911yescharacteristic
737C2×C4⋊C4—22no—
738C2×C4⋊C4—22no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—41no—
741C2×C4⋊C4—41no—
742C2×C4⋊C4—41no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4D4×C10914yes—
788C2×C42—22no—
789C2×C42—41no—
790C2×C42—41no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—41no—
798#95—41no—
799#95—41no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95D4×C10914yescomplemented
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24C2×D4×C10912yes—
848C24#41×C10912yes—
849C24#41×C10912yes—
850C24C24×C10911yescharacteristic
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4C2×D4×C10912yes—
949C22×C4C2×D4×C10912yes—
950C22×C4C2×D4×C10912yes—
951C22×C4C2×D4×C10912yes—
952C22×C4C2×D4×C10912yes—
953C22×C4#41×C10912yes—
954C22×C4#41×C10912yes—
955C22×C4#41×C10912yes—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C22⋊C4—28no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C42—44no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23C22×D4×C10911yescharacteristic
1080C23C22×D4×C10911yescharacteristic
1081C23C2×#41×C10911yescharacteristic
1082C23C2×#41×C10911yescharacteristic
1083C23C2×#41×C10911yescharacteristic
1084C23C2×#41×C10911yescharacteristic
1085C23C2×#41×C10911yescharacteristic
1086C23H(5,𝔽2)×C10911yescharacteristic
1087C23H(5,𝔽2)×C10911yescharacteristic
1088C23H(5,𝔽2)×C10911yescharacteristic
1089C23H(5,𝔽2)×C10911yescharacteristic
1090C23H(5,𝔽2)×C10911yescharacteristic
1091C23H(5,𝔽2)×C10911yescharacteristic
1092C23H(5,𝔽2)×C10911yescharacteristic
1093C23H(5,𝔽2)×C10911yescharacteristic
1094D4—416no—
1095D4—416no—
1096D4—416no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22#525×C10911yescharacteristic
1227C22#529×C10911yescharacteristic
1228C22#532×C10911yescharacteristic
1229C22#534×C10911yescharacteristic
1230C22#535×C10911yescharacteristic
1231C22#535×C10911yescharacteristic
1232C22#535×C10911yescharacteristic
1233C22#538×C10911yescharacteristic
1234C22#538×C10911yescharacteristic
1235C22#538×C10911yescharacteristic
1236C22#538×C10911yescharacteristic
1237C22#538×C10911yescharacteristic
1238C22#538×C10911yescharacteristic
1239C22#538×C10911yescharacteristic
1240C22#538×C10911yescharacteristic
1241C22#540×C10911yescharacteristic
1242C22#540×C10911yescharacteristic
1243C22#540×C10911yescharacteristic
1244C22#540×C10911yescharacteristic
1245C22D42×C10911yescharacteristic
1246C22#546×C10911yescharacteristic
1247C22#546×C10911yescharacteristic
1248C22#546×C10911yescharacteristic
1249C22#546×C10911yescharacteristic
1250C22#546×C10911yescharacteristic
1251C22#550×C10911yescharacteristic
1252C22#551×C10911yescharacteristic
1253C22#551×C10911yescharacteristic
1254C22#553×C10911yescharacteristic
1255C22#553×C10911yescharacteristic
1256C22#553×C10911yescharacteristic
1257C22#560×C10911yescharacteristic
1258C22#560×C10911yescharacteristic
1259C22#560×C10911yescharacteristic
1260C22H(3,𝔽4)×C10911yescharacteristic
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C2—82no—
1274C2—82no—
1275C2—82no—
1276C2C109×#246411yescharacteristic
1277C2C109×#247111yescharacteristic
1278C2C109×#255911yescharacteristic
1279C2C109×#263111yescharacteristic
1280C2C109×#264811yescharacteristic
1281C2C109×#266111yescharacteristic
1282C2C109×#267011yescharacteristic
1283C2C109×#267311yescharacteristic
1284C2C109×#268511yescharacteristic
1285C2C109×#269711yescharacteristic
1286C2C109×#270311yescharacteristic
1287C2C109×#271411yescharacteristic
1288C2C109×#275311yescharacteristic
1289C2C109×#277811yescharacteristic
1290C2C109×#282811yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutator, Frattini, cosocleC24C24×C109
prime radicalC2×#392×C109C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#397×C109C2semidirect
2. C2×#394×C109C2semidirect
4. C2×#388×C109C2semidirect
5. C109×#1443C2semidirect
6. C109×#1442C2semidirect
7. C109×#1439C2semidirect
8. C109×#1439C2semidirect
9. C109×#1438C2semidirect
10. C109×#1438C2semidirect
11. C109×#1438C2semidirect
12. C109×#1438C2semidirect
13. C109×#1438C2semidirect
14. C109×#1437C2semidirect
15. C109×#1437C2semidirect
158. #95×C109D4semidirect
627. #16535C109direct (N × H)
646. C2×#397C2×C109semidirect
647. C2×#394C2×C109semidirect
649. C2×#388C2×C109semidirect
650. #1443C2×C109semidirect
651. #1442C2×C109semidirect
652. #1439C2×C109semidirect
653. #1439C2×C109semidirect
654. #1438C2×C109semidirect
655. #1438C2×C109semidirect
656. #1438C2×C109semidirect
657. #1438C2×C109semidirect
658. #1438C2×C109semidirect
659. #1437C2×C109semidirect
660. #1437C2×C109semidirect
661. C109#16535direct (N × H)
804. #95D4×C109semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#397×C1092
C2×#394×C1092
C2×#392×C1092
C2×#388×C1092
C109×#14432
C109×#14422
C109×#14392
C109×#14382
C109×#14372
#16535109