Finite Group Databasebeta

← C109×#14359 #42132353

Subgroups — C109×#14359 #42132353

Order 27904.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C109C211yesmaximal, characteristic
2C2×#388×C109C211yesmaximal, characteristic, complemented
3C2×#386×C109C211yesmaximal, characteristic
4C2×#385×C109C211yesmaximal, characteristic, complemented
5C2×#380×C109C211yesmaximal, characteristic, complemented
6C109×#1445C211yesmaximal, characteristic, complemented
7C109×#1441C211yesmaximal, characteristic, complemented
8C109×#1441C211yesmaximal, characteristic, complemented
9C109×#1440C211yesmaximal, characteristic, complemented
10C109×#1439C211yesmaximal, characteristic, complemented
11C109×#1438C211yesmaximal, characteristic
12C109×#1437C211yesmaximal, characteristic, complemented
13C109×C4⋊#95C211yesmaximal, characteristic, complemented
14C109×C22⋊#95C211yesmaximal, characteristic, complemented
15C109×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C24×C4×C109C2211yescharacteristic
18C24×C4×C109C2211yescharacteristic
19C2×#123×C109—24no—
20C2×#123×C109—24no—
21C2×#123×C109C418yescomplemented
22C22×C4⋊C4×C109C2211yescharacteristic
23C22×C4⋊C4×C109C2211yescharacteristic
24C22×C4⋊C4×C109C2211yescharacteristic
25C22×C4⋊C4×C109C2211yescharacteristic
26C22×C4⋊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×C22⋊C4×C109C2211yescharacteristic
37C22×C42×C109C2211yescharacteristic
38#388×C109—24no—
39#386×C109—24no—
40#385×C109—24no—
41#380×C109—24no—
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
55C2×#95×C109C2211yescharacteristic
56C2×#95×C109C2211yescharacteristic
57C2×#95×C109C2211yescharacteristic
58C25×C109C2311yescharacteristic
59C25×C109C2311yescharacteristic
60C22×D4×C109—22no—
61C22×D4×C109—22no—
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—41no—
65C22×D4×C109—41no—
66C22×D4×C109C2×C414yes—
67C23×C4×C109—22no—
68C23×C4×C109—22no—
69C23×C4×C109—22no—
70C23×C4×C109—22no—
71C23×C4×C109—22no—
72C23×C4×C109—22no—
73C23×C4×C109—22no—
74C23×C4×C109—41no—
75C23×C4×C109—41no—
76C23×C4×C109—41no—
77C23×C4×C109—41no—
78C23×C4×C109—41no—
79C23×C4×C109—41no—
80C23×C4×C109C2×C414yescomplemented
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
91C23×C4×C109C2311yescharacteristic
92C23×C4×C109C2311yescharacteristic
93C23×C4×C109C2311yescharacteristic
94#123×C109—232no—
95C2×C4⋊C4×C109—22no—
96C2×C4⋊C4×C109—22no—
97C2×C4⋊C4×C109—22no—
98C2×C4⋊C4×C109—22no—
99C2×C4⋊C4×C109—22no—
100C2×C4⋊C4×C109—22no—
101C2×C4⋊C4×C109—22no—
102C2×C4⋊C4×C109—22no—
103C2×C4⋊C4×C109—22no—
104C2×C4⋊C4×C109—22no—
105C2×C4⋊C4×C109—41no—
106C2×C4⋊C4×C109—41no—
107C2×C4⋊C4×C109—41no—
108C2×C4⋊C4×C109C2×C414yescomplemented
109C2×C4⋊C4×C109C2×C414yescomplemented
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—22no—
118C2×C22⋊C4×C109—22no—
119C2×C22⋊C4×C109—22no—
120C2×C22⋊C4×C109—22no—
121C2×C22⋊C4×C109—22no—
122C2×C22⋊C4×C109—22no—
123C2×C22⋊C4×C109—22no—
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×C109C2×C414yes—
135C2×C22⋊C4×C109C2×C414yes—
136C2×C22⋊C4×C109C2×C414yescomplemented
137C2×C22⋊C4×C109D414yes—
138C2×C22⋊C4×C109D414yes—
139C2×C22⋊C4×C109D414yes—
140C2×C42×C109—22no—
141C2×C42×C109—22no—
142C2×C42×C109—41no—
143#95×C109—22no—
144#95×C109—22no—
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×C109—41no—
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×C109C22×C412yes—
184C24×C109C22×C412yes—
185C24×C109C2×D412yes—
186C24×C109C2×D412yes—
187C24×C109C2×D412yes—
188C24×C109#4112yes—
189C24×C109C2411yescharacteristic
190C2×D4×C109—28no—
191C2×D4×C109—28no—
192C2×D4×C109—44no—
193C2×D4×C109—44no—
194C2×D4×C109—44no—
195C2×D4×C109—44no—
196C2×D4×C109—44no—
197C22×C4×C109—21no—
198C22×C4×C109—21no—
199C22×C4×C109—21no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—28no—
206C22×C4×C109—21no—
207C22×C4×C109—21no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—21no—
211C22×C4×C109—21no—
212C22×C4×C109—21no—
213C22×C4×C109—21no—
214C22×C4×C109—21no—
215C22×C4×C109—21no—
216C22×C4×C109—21no—
217C22×C4×C109—21no—
218C22×C4×C109—21no—
219C22×C4×C109—21no—
220C22×C4×C109—21no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
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—28no—
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—44no—
278C22×C4×C109—44no—
279C22×C4×C109—44no—
280C22×C4×C109—44no—
281C22×C4×C109—44no—
282C22×C4×C109—44no—
283C22×C4×C109—44no—
284C22×C4×C109—44no—
285C22×C4×C109—44no—
286C22×C4×C109—44no—
287C22×C4×C109—44no—
288C22×C4×C109—44no—
289C22×C4×C109C22×C412yes—
290C22×C4×C109C22×C412yes—
291C22×C4×C109C22×C412yes—
292C22×C4×C109C22×C412yes—
293C22×C4×C109C22×C412yes—
294C22×C4×C109C2×D412yes—
295C22×C4×C109C2×D412yes—
296C22×C4×C109C2×D412yes—
297C22×C4×C109C2×D412yes—
298C22×C4×C109C2×D412yes—
299C22×C4×C109C2×D412yes—
300C22×C4×C109#4112yes—
301C22×C4×C109#4112yes—
302C4⋊C4×C109—28no—
303C4⋊C4×C109—28no—
304C4⋊C4×C109—44no—
305C4⋊C4×C109—44no—
306C4⋊C4×C109—44no—
307C22⋊C4×C109—28no—
308C22⋊C4×C109—28no—
309C22⋊C4×C109—44no—
310C22⋊C4×C109—44no—
311C22⋊C4×C109—44no—
312C22⋊C4×C109—44no—
313C22⋊C4×C109—44no—
314C22⋊C4×C109—44no—
315C22⋊C4×C109—44no—
316C22⋊C4×C109C22⋊C4116yescomplemented
317C42×C109—44no—
318C23×C109—22no—
319C23×C109—22no—
320C23×C109—22no—
321C23×C109—22no—
322C23×C109—22no—
323C23×C109—22no—
324C23×C109—22no—
325C23×C109—22no—
326C23×C109—22no—
327C23×C109—22no—
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—22no—
350C23×C109—22no—
351C23×C109—22no—
352C23×C109—22no—
353C23×C109—22no—
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×C109C2×C22⋊C414yes—
387C23×C109C4×D414yes—
388C23×C109C23×C411yescharacteristic
389C23×C109C22×D411yescharacteristic
390C23×C109C22×D411yescharacteristic
391C23×C109C22×D411yescharacteristic
392C23×C109C2×#4111yescharacteristic
393C23×C109C2×#4111yescharacteristic
394C23×C109C2×#4111yescharacteristic
395C23×C109H(5,𝔽2)11yescharacteristic
396C23×C109H(5,𝔽2)11yescharacteristic
397C23×C109H(5,𝔽2)11yescharacteristic
398C23×C109H(5,𝔽2)11yescharacteristic
399C23×C109H(5,𝔽2)11yescharacteristic
400C23×C1092−1+411yescharacteristic
401C23×C1092−1+411yescharacteristic
402C23×C1092−1+411yescharacteristic
403D4×C109—416no—
404C2×C4×C109—22no—
405C2×C4×C109—22no—
406C2×C4×C109—22no—
407C2×C4×C109—22no—
408C2×C4×C109—22no—
409C2×C4×C109—22no—
410C2×C4×C109—22no—
411C2×C4×C109—22no—
412C2×C4×C109—22no—
413C2×C4×C109—22no—
414C2×C4×C109—22no—
415C2×C4×C109—22no—
416C2×C4×C109—22no—
417C2×C4×C109—22no—
418C2×C4×C109—22no—
419C2×C4×C109—22no—
420C2×C4×C109—22no—
421C2×C4×C109—22no—
422C2×C4×C109—22no—
423C2×C4×C109—22no—
424C2×C4×C109—22no—
425C2×C4×C109—22no—
426C2×C4×C109—22no—
427C2×C4×C109—22no—
428C2×C4×C109—22no—
429C2×C4×C109—22no—
430C2×C4×C109—22no—
431C2×C4×C109—22no—
432C2×C4×C109—22no—
433C2×C4×C109—22no—
434C2×C4×C109—22no—
435C2×C4×C109—22no—
436C2×C4×C109—22no—
437C2×C4×C109—416no—
438C2×C4×C109—416no—
439C2×C4×C109—41no—
440C2×C4×C109—41no—
441C2×C4×C109—41no—
442C2×C4×C109—41no—
443C2×C4×C109—41no—
444C2×C4×C109—41no—
445C2×C4×C109—41no—
446C2×C4×C109—41no—
447C2×C4×C109—41no—
448C2×C4×C109—41no—
449C2×C4×C109—41no—
450C2×C4×C109—41no—
451C2×C4×C109—41no—
452C2×C4×C109—41no—
453C2×C4×C109—41no—
454C2×C4×C109—41no—
455C2×C4×C109—41no—
456C2×C4×C109—41no—
457C2×C4×C109—41no—
458C2×C4×C109—41no—
459C2×C4×C109—41no—
460C2×C4×C109—41no—
461C2×C4×C109—41no—
462C2×C4×C109—41no—
463C2×C4×C109—41no—
464C2×C4×C109—41no—
465C2×C4×C109—41no—
466C2×C4×C109—41no—
467C2×C4×C109—41no—
468C2×C4×C109—41no—
469C2×C4×C109—41no—
470C2×C4×C109—41no—
471C2×C4×C109—41no—
472C2×C4×C109—41no—
473C2×C4×C109—41no—
474C2×C4×C109—41no—
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×C109C2×C22⋊C414yes—
496C2×C4×C109C2×C22⋊C414yes—
497C22×C109—24no—
498C22×C109—24no—
499C22×C109—24no—
500C22×C109—24no—
501C22×C109—24no—
502C22×C109—24no—
503C22×C109—42no—
504C22×C109—42no—
505C22×C109—42no—
506C22×C109—42no—
507C22×C109—42no—
508C22×C109—42no—
509C22×C109—42no—
510C22×C109—42no—
511C22×C109—42no—
512C22×C109—42no—
513C22×C109—42no—
514C22×C109—42no—
515C22×C109—42no—
516C22×C109—42no—
517C22×C109—42no—
518C22×C109—42no—
519C22×C109—42no—
520C22×C109—42no—
521C22×C109—42no—
522C22×C109—42no—
523C22×C109—42no—
524C22×C109—42no—
525C22×C109—42no—
526C22×C109—42no—
527C22×C109C22×C22⋊C411yescharacteristic
528C22×C109C2×C4×D411yescharacteristic
529C22×C109C4×#4111yescharacteristic
530C22×C109#51811yescharacteristic
531C22×C109#52011yescharacteristic
532C22×C109#52011yescharacteristic
533C22×C109#52011yescharacteristic
534C22×C109#53411yescharacteristic
535C22×C109#53511yescharacteristic
536C22×C109#53611yescharacteristic
537C22×C109#53611yescharacteristic
538C22×C109#53711yescharacteristic
539C22×C109#53711yescharacteristic
540C22×C109#53811yescharacteristic
541C22×C109#53911yescharacteristic
542C22×C109#53911yescharacteristic
543C22×C109#53911yescharacteristic
544C22×C109#54011yescharacteristic
545C22×C109#54211yescharacteristic
546C22×C109D4211yescharacteristic
547C22×C109D4211yescharacteristic
548C22×C109#54611yescharacteristic
549C22×C109#54611yescharacteristic
550C22×C109#54611yescharacteristic
551C22×C109#54611yescharacteristic
552C22×C109#54611yescharacteristic
553C22×C109#54711yescharacteristic
554C22×C109#54711yescharacteristic
555C22×C109#54711yescharacteristic
556C22×C109#55111yescharacteristic
557C22×C109#55211yescharacteristic
558C22×C109#56011yescharacteristic
559C22×C109#56211yescharacteristic
560C22×C109#56211yescharacteristic
561C22×C109#56311yescharacteristic
562C4×C109—24no—
563C4×C109—24no—
564C4×C109—42no—
565C4×C109—42no—
566C4×C109—42no—
567C4×C109—42no—
568C4×C109—42no—
569C4×C109—42no—
570C4×C109—42no—
571C4×C109—81no—
572C4×C109—81no—
573C4×C109—81no—
574C4×C109—81no—
575#14359C10911yesmaximal, characteristic, direct product factor, Sylow
576C2×C109—44no—
577C2×C109—44no—
578C2×C109#231111yescharacteristic
579C2×C109#232211yescharacteristic
580C2×C109#233511yescharacteristic
581C2×C109D4×C22⋊C411yescharacteristic
582C2×C109#233911yescharacteristic
583C2×C109#235911yescharacteristic
584C2×C109#237611yescharacteristic
585C2×C109#267111yescharacteristic
586C2×C109#267211yescharacteristic
587C2×C109#267811yescharacteristic
588C2×C109#268011yescharacteristic
589C2×C109#268711yescharacteristic
590C2×C109#269311yescharacteristic
591C2×C109#269511yescharacteristic
592C2×C109#270611yescharacteristic
593C22×#123C2×C10911yescharacteristic
594C2×#388C2×C10911yescharacteristic, complemented
595C2×#386C2×C10911yescharacteristic
596C2×#385C2×C10911yescharacteristic, complemented
597C2×#380C2×C10911yescharacteristic, complemented
598#1445C2×C10911yescharacteristic, complemented
599#1441C2×C10911yescharacteristic, complemented
600#1441C2×C10911yescharacteristic, complemented
601#1440C2×C10911yescharacteristic, complemented
602#1439C2×C10911yescharacteristic, complemented
603#1438C2×C10911yescharacteristic
604#1437C2×C10911yescharacteristic, complemented
605C4⋊#95C2×C10911yescharacteristic, complemented
606C22⋊#95C2×C10911yescharacteristic, complemented
607C22⋊#95C2×C10911yescharacteristic, complemented
608C109#1435911yescharacteristic, direct product factor, Sylow
609C23×D4C22×C10911yescharacteristic
610C24×C4C22×C10911yescharacteristic
611C24×C4C22×C10911yescharacteristic
612C2×#123—24no—
613C2×#123—24no—
614C2×#123C4×C10918yescomplemented
615C22×C4⋊C4C22×C10911yescharacteristic
616C22×C4⋊C4C22×C10911yescharacteristic
617C22×C4⋊C4C22×C10911yescharacteristic
618C22×C4⋊C4C22×C10911yescharacteristic
619C22×C4⋊C4C22×C10911yescharacteristic
620C22×C22⋊C4C22×C10911yescharacteristic
621C22×C22⋊C4C22×C10911yescharacteristic
622C22×C22⋊C4C22×C10911yescharacteristic
623C22×C22⋊C4C22×C10911yescharacteristic
624C22×C22⋊C4C22×C10911yescharacteristic
625C22×C22⋊C4C22×C10911yescharacteristic
626C22×C22⋊C4C22×C10911yescharacteristic
627C22×C22⋊C4C22×C10911yescharacteristic
628C22×C22⋊C4C22×C10911yescharacteristic
629C22×C22⋊C4C22×C10911yescharacteristic
630C22×C42C22×C10911yescharacteristic
631#388—24no—
632#386—24no—
633#385—24no—
634#380—24no—
635C2×#95C22×C10911yescharacteristic
636C2×#95C22×C10911yescharacteristic
637C2×#95C22×C10911yescharacteristic
638C2×#95C22×C10911yescharacteristic
639C2×#95C22×C10911yescharacteristic
640C2×#95C22×C10911yescharacteristic
641C2×#95C22×C10911yescharacteristic
642C2×#95C22×C10911yescharacteristic
643C2×#95C22×C10911yescharacteristic
644C2×#95C22×C10911yescharacteristic
645C2×#95C22×C10911yescharacteristic
646C2×#95C22×C10911yescharacteristic
647C2×#95C22×C10911yescharacteristic
648C2×#95C22×C10911yescharacteristic
649C2×#95C22×C10911yescharacteristic
650C2×#95C22×C10911yescharacteristic
651C25C23×C10911yescharacteristic
652C25C23×C10911yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C2×C4×C10914yes—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—41no—
668C23×C4—41no—
669C23×C4—41no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4C2×C4×C10914yescomplemented
674C23×C4C23×C10911yescharacteristic
675C23×C4C23×C10911yescharacteristic
676C23×C4C23×C10911yescharacteristic
677C23×C4C23×C10911yescharacteristic
678C23×C4C23×C10911yescharacteristic
679C23×C4C23×C10911yescharacteristic
680C23×C4C23×C10911yescharacteristic
681C23×C4C23×C10911yescharacteristic
682C23×C4C23×C10911yescharacteristic
683C23×C4C23×C10911yescharacteristic
684C23×C4C23×C10911yescharacteristic
685C23×C4C23×C10911yescharacteristic
686C23×C4C23×C10911yescharacteristic
687#123—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4—41no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4C2×C4×C10914yescomplemented
702C2×C4⋊C4C2×C4×C10914yescomplemented
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4C2×C4×C10914yes—
728C2×C22⋊C4C2×C4×C10914yes—
729C2×C22⋊C4C2×C4×C10914yescomplemented
730C2×C22⋊C4D4×C10914yes—
731C2×C22⋊C4D4×C10914yes—
732C2×C22⋊C4D4×C10914yes—
733C2×C42—22no—
734C2×C42—22no—
735C2×C42—41no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—41no—
745#95—41no—
746#95—41no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95—41no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C22×C4×C10912yes—
777C24C22×C4×C10912yes—
778C24C2×D4×C10912yes—
779C24C2×D4×C10912yes—
780C24C2×D4×C10912yes—
781C24#41×C10912yes—
782C24C24×C10911yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—28no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—28no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4C22×C4×C10912yes—
883C22×C4C22×C4×C10912yes—
884C22×C4C22×C4×C10912yes—
885C22×C4C22×C4×C10912yes—
886C22×C4C22×C4×C10912yes—
887C22×C4C2×D4×C10912yes—
888C22×C4C2×D4×C10912yes—
889C22×C4C2×D4×C10912yes—
890C22×C4C2×D4×C10912yes—
891C22×C4C2×D4×C10912yes—
892C22×C4C2×D4×C10912yes—
893C22×C4#41×C10912yes—
894C22×C4#41×C10912yes—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4C22⋊C4×C109116yescomplemented
910C42—44no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C2×C22⋊C4×C10914yes—
980C23C4×D4×C10914yes—
981C23C23×C4×C10911yescharacteristic
982C23C22×D4×C10911yescharacteristic
983C23C22×D4×C10911yescharacteristic
984C23C22×D4×C10911yescharacteristic
985C23C2×#41×C10911yescharacteristic
986C23C2×#41×C10911yescharacteristic
987C23C2×#41×C10911yescharacteristic
988C23H(5,𝔽2)×C10911yescharacteristic
989C23H(5,𝔽2)×C10911yescharacteristic
990C23H(5,𝔽2)×C10911yescharacteristic
991C23H(5,𝔽2)×C10911yescharacteristic
992C23H(5,𝔽2)×C10911yescharacteristic
993C232−1+4×C10911yescharacteristic
994C232−1+4×C10911yescharacteristic
995C232−1+4×C10911yescharacteristic
996D4—416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—416no—
1031C2×C4—416no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4C2×C22⋊C4×C10914yes—
1089C2×C4C2×C22⋊C4×C10914yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C22×C22⋊C4×C10911yescharacteristic
1121C22C2×C4×D4×C10911yescharacteristic
1122C22C4×#41×C10911yescharacteristic
1123C22#518×C10911yescharacteristic
1124C22#520×C10911yescharacteristic
1125C22#520×C10911yescharacteristic
1126C22#520×C10911yescharacteristic
1127C22#534×C10911yescharacteristic
1128C22#535×C10911yescharacteristic
1129C22#536×C10911yescharacteristic
1130C22#536×C10911yescharacteristic
1131C22#537×C10911yescharacteristic
1132C22#537×C10911yescharacteristic
1133C22#538×C10911yescharacteristic
1134C22#539×C10911yescharacteristic
1135C22#539×C10911yescharacteristic
1136C22#539×C10911yescharacteristic
1137C22#540×C10911yescharacteristic
1138C22#542×C10911yescharacteristic
1139C22D42×C10911yescharacteristic
1140C22D42×C10911yescharacteristic
1141C22#546×C10911yescharacteristic
1142C22#546×C10911yescharacteristic
1143C22#546×C10911yescharacteristic
1144C22#546×C10911yescharacteristic
1145C22#546×C10911yescharacteristic
1146C22#547×C10911yescharacteristic
1147C22#547×C10911yescharacteristic
1148C22#547×C10911yescharacteristic
1149C22#551×C10911yescharacteristic
1150C22#552×C10911yescharacteristic
1151C22#560×C10911yescharacteristic
1152C22#562×C10911yescharacteristic
1153C22#562×C10911yescharacteristic
1154C22#563×C10911yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—44no—
1170C2C109×#231111yescharacteristic
1171C2C109×#232211yescharacteristic
1172C2C109×#233511yescharacteristic
1173C2D4×C22⋊C4×C10911yescharacteristic
1174C2C109×#233911yescharacteristic
1175C2C109×#235911yescharacteristic
1176C2C109×#237611yescharacteristic
1177C2C109×#267111yescharacteristic
1178C2C109×#267211yescharacteristic
1179C2C109×#267811yescharacteristic
1180C2C109×#268011yescharacteristic
1181C2C109×#268711yescharacteristic
1182C2C109×#269311yescharacteristic
1183C2C109×#269511yescharacteristic
1184C2C109×#270611yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutatorC23C23×C4×C109
Frattini, cosocleC24C24×C109
prime radicalC23×D4×C109C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C109C2semidirect
4. C2×#385×C109C2semidirect
5. C2×#380×C109C2semidirect
6. C109×#1445C2semidirect
7. C109×#1441C2semidirect
8. C109×#1441C2semidirect
9. C109×#1440C2semidirect
10. C109×#1439C2semidirect
12. C109×#1437C2semidirect
13. C109×C4⋊#95C2semidirect
14. C109×C22⋊#95C2semidirect
15. C109×C22⋊#95C2semidirect
21. C2×#123×C109C4semidirect
80. C23×C4×C109C2×C4semidirect
108. C2×C4⋊C4×C109C2×C4semidirect
109. C2×C4⋊C4×C109C2×C4semidirect
136. C2×C22⋊C4×C109C2×C4semidirect
316. C22⋊C4×C109C22⋊C4semidirect
575. #14359C109direct (N × H)
594. C2×#388C2×C109semidirect
596. C2×#385C2×C109semidirect
597. C2×#380C2×C109semidirect
598. #1445C2×C109semidirect
599. #1441C2×C109semidirect
600. #1441C2×C109semidirect
601. #1440C2×C109semidirect
602. #1439C2×C109semidirect
604. #1437C2×C109semidirect
605. C4⋊#95C2×C109semidirect
606. C22⋊#95C2×C109semidirect
607. C22⋊#95C2×C109semidirect
608. C109#14359direct (N × H)
614. C2×#123C4×C109semidirect
673. C23×C4C2×C4×C109semidirect
701. C2×C4⋊C4C2×C4×C109semidirect
702. C2×C4⋊C4C2×C4×C109semidirect
729. C2×C22⋊C4C2×C4×C109semidirect
909. C22⋊C4C22⋊C4×C109semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1092
C2×#388×C1092
C2×#386×C1092
C2×#385×C1092
C2×#380×C1092
C109×#14452
C109×#14412
C109×#14402
C109×#14392
C109×#14382
C109×#14372
C109×C4⋊#952
C109×C22⋊#952
#14359109