Finite Group Databasebeta

← C109×#14405 #42132399

Subgroups — C109×#14405 #42132399

Order 27904.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C109C211yesmaximal, characteristic, complemented
2C2×#388×C109C211yesmaximal, characteristic
3C2×#388×C109C211yesmaximal, characteristic
4C2×#385×C109C211yesmaximal, characteristic
5C2×#385×C109C211yesmaximal, characteristic
6C2×#385×C109C211yesmaximal, characteristic
7C2×#384×C109C211yesmaximal, characteristic, complemented
8C109×#1444C211yesmaximal, characteristic, complemented
9C109×#1444C211yesmaximal, characteristic, complemented
10C109×#1442C211yesmaximal, characteristic, complemented
11C109×#1441C211yesmaximal, characteristic, complemented
12C109×#1439C211yesmaximal, characteristic
13C109×#1439C211yesmaximal, characteristic
14C109×#1436C211yesmaximal, characteristic, complemented
15C109×#1434C211yesmaximal, characteristic, complemented
16C24×C4×C109C2211yescharacteristic
17C22×C4⋊C4×C109C2211yescharacteristic
18C22×C4⋊C4×C109C2211yescharacteristic
19C22×C4⋊C4×C109C2211yescharacteristic
20C22×C4⋊C4×C109C2211yescharacteristic
21C22×C4⋊C4×C109C2211yescharacteristic
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×C42×C109C2211yescharacteristic
34C22×C42×C109C2211yescharacteristic
35#389×C109—24no—
36#388×C109—24no—
37#388×C109C418yescomplemented
38#385×C109—24no—
39#385×C109—24no—
40#385×C109—24no—
41#384×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
59C23×C4×C109—22no—
60C23×C4×C109—22no—
61C23×C4×C109—22no—
62C23×C4×C109—41no—
63C23×C4×C109—41no—
64C23×C4×C109—41no—
65C23×C4×C109—41no—
66C23×C4×C109C2311yescharacteristic
67C23×C4×C109C2311yescharacteristic
68C23×C4×C109C2311yescharacteristic
69C23×C4×C109C2311yescharacteristic
70C23×C4×C109C2311yescharacteristic
71C23×C4×C109C2311yescharacteristic
72C23×C4×C109C2311yescharacteristic
73C23×C4×C109C2311yescharacteristic
74C23×C4×C109C2311yescharacteristic
75C23×C4×C109C2311yescharacteristic
76C23×C4×C109C2311yescharacteristic
77C23×C4×C109C2311yescharacteristic
78C23×C4×C109C2311yescharacteristic
79C23×C4×C109C2311yescharacteristic
80C2×C4⋊C4×C109—22no—
81C2×C4⋊C4×C109—22no—
82C2×C4⋊C4×C109—22no—
83C2×C4⋊C4×C109—22no—
84C2×C4⋊C4×C109—22no—
85C2×C4⋊C4×C109—22no—
86C2×C4⋊C4×C109—22no—
87C2×C4⋊C4×C109—22no—
88C2×C4⋊C4×C109—22no—
89C2×C4⋊C4×C109—22no—
90C2×C4⋊C4×C109—22no—
91C2×C4⋊C4×C109—22no—
92C2×C4⋊C4×C109—22no—
93C2×C4⋊C4×C109—22no—
94C2×C4⋊C4×C109—22no—
95C2×C4⋊C4×C109—22no—
96C2×C4⋊C4×C109—41no—
97C2×C4⋊C4×C109—41no—
98C2×C4⋊C4×C109—41no—
99C2×C4⋊C4×C109—41no—
100C2×C4⋊C4×C109—41no—
101C2×C4⋊C4×C109—41no—
102C2×C4⋊C4×C109—41no—
103C2×C4⋊C4×C109—41no—
104C2×C4⋊C4×C109—41no—
105C2×C4⋊C4×C109—41no—
106C2×C4⋊C4×C109—41no—
107C2×C4⋊C4×C109—41no—
108C2×C4⋊C4×C109C2×C414yescomplemented
109C2×C4⋊C4×C109D414yes—
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—41no—
120C2×C22⋊C4×C109—41no—
121C2×C22⋊C4×C109—41no—
122C2×C22⋊C4×C109—41no—
123C2×C22⋊C4×C109C2×C414yes—
124C2×C22⋊C4×C109C2×C414yes—
125C2×C22⋊C4×C109C2×C414yes—
126C2×C22⋊C4×C109D414yes—
127C2×C22⋊C4×C109Q814yes—
128C2×C42×C109—22no—
129C2×C42×C109—22no—
130C2×C42×C109—22no—
131C2×C42×C109—22no—
132C2×C42×C109—41no—
133C2×C42×C109C2×C414yescomplemented
134#95×C109—22no—
135#95×C109—22no—
136#95×C109—22no—
137#95×C109—22no—
138#95×C109—22no—
139#95×C109—22no—
140#95×C109—22no—
141#95×C109—22no—
142#95×C109—22no—
143#95×C109—22no—
144#95×C109—41no—
145#95×C109—41no—
146#95×C109—41no—
147#95×C109C2×C414yescomplemented
148#95×C109C2×C414yescomplemented
149#95×C109D414yes—
150C24×C109—21no—
151C24×C109—21no—
152C24×C109—21no—
153C24×C109—21no—
154C24×C109—21no—
155C24×C109—21no—
156C24×C109—21no—
157C24×C109—21no—
158C24×C109—21no—
159C24×C109—21no—
160C24×C109—21no—
161C24×C109—21no—
162C24×C109C22×C412yes—
163C24×C109C2×D412yes—
164C24×C109C2×Q812yes—
165C24×C109C2411yescharacteristic
166C22×C4×C109—21no—
167C22×C4×C109—21no—
168C22×C4×C109—21no—
169C22×C4×C109—21no—
170C22×C4×C109—21no—
171C22×C4×C109—21no—
172C22×C4×C109—21no—
173C22×C4×C109—21no—
174C22×C4×C109—21no—
175C22×C4×C109—21no—
176C22×C4×C109—21no—
177C22×C4×C109—21no—
178C22×C4×C109—21no—
179C22×C4×C109—21no—
180C22×C4×C109—21no—
181C22×C4×C109—21no—
182C22×C4×C109—21no—
183C22×C4×C109—21no—
184C22×C4×C109—21no—
185C22×C4×C109—21no—
186C22×C4×C109—21no—
187C22×C4×C109—21no—
188C22×C4×C109—21no—
189C22×C4×C109—21no—
190C22×C4×C109—21no—
191C22×C4×C109—21no—
192C22×C4×C109—21no—
193C22×C4×C109—21no—
194C22×C4×C109—21no—
195C22×C4×C109—21no—
196C22×C4×C109—21no—
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—21no—
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—44no—
247C22×C4×C109—44no—
248C22×C4×C109—44no—
249C22×C4×C109—44no—
250C22×C4×C109—44no—
251C22×C4×C109—44no—
252C22×C4×C109—44no—
253C22×C4×C109C22×C412yes—
254C22×C4×C109C22×C412yes—
255C22×C4×C109C22×C412yes—
256C22×C4×C109C22×C412yes—
257C22×C4×C109C22×C412yes—
258C22×C4×C109C22×C412yes—
259C22×C4×C109C2×D412yes—
260C22×C4×C109C2×D412yes—
261C22×C4×C109C2×D412yes—
262C22×C4×C109C2×D412yes—
263C22×C4×C109C2×D412yes—
264C22×C4×C109C2×D412yes—
265C22×C4×C109C2×D412yes—
266C22×C4×C109C2×D412yes—
267C22×C4×C109C2×Q812yes—
268C22×C4×C109C2×Q812yes—
269C22×C4×C109#4112yes—
270C22×C4×C109#4112yes—
271C4⋊C4×C109—28no—
272C4⋊C4×C109—44no—
273C4⋊C4×C109—44no—
274C4⋊C4×C109—44no—
275C4⋊C4×C109—44no—
276C4⋊C4×C109—44no—
277C4⋊C4×C109—44no—
278C4⋊C4×C109—44no—
279C4⋊C4×C109—44no—
280C4⋊C4×C109—44no—
281C22⋊C4×C109—28no—
282C22⋊C4×C109—28no—
283C22⋊C4×C109—44no—
284C22⋊C4×C109—44no—
285C22⋊C4×C109—44no—
286C22⋊C4×C109C4⋊C4116yescomplemented
287C42×C109—28no—
288C42×C109—44no—
289C23×C109—22no—
290C23×C109—22no—
291C23×C109—22no—
292C23×C109—22no—
293C23×C109—22no—
294C23×C109—22no—
295C23×C109—22no—
296C23×C109—22no—
297C23×C109—22no—
298C23×C109—22no—
299C23×C109—22no—
300C23×C109—22no—
301C23×C109—22no—
302C23×C109—22no—
303C23×C109—22no—
304C23×C109—22no—
305C23×C109—22no—
306C23×C109—22no—
307C23×C109—41no—
308C23×C109—41no—
309C23×C109—41no—
310C23×C109—41no—
311C23×C109—41no—
312C23×C109—41no—
313C23×C109—41no—
314C23×C109—41no—
315C23×C109—41no—
316C23×C109—41no—
317C23×C109—41no—
318C23×C109—41no—
319C23×C109—41no—
320C23×C109—41no—
321C23×C109—41no—
322C23×C109—41no—
323C23×C109C2×C4⋊C414yes—
324C23×C109C23×C411yescharacteristic
325C23×C109C22×D411yescharacteristic
326C23×C109C22×D411yescharacteristic
327C23×C109C22×D411yescharacteristic
328C23×C109C22×Q811yescharacteristic
329C23×C109C2×#4111yescharacteristic
330C23×C109C2×#4111yescharacteristic
331C23×C109H(5,𝔽2)11yescharacteristic
332C23×C109H(5,𝔽2)11yescharacteristic
333C23×C109H(5,𝔽2)11yescharacteristic
334C23×C109H(5,𝔽2)11yescharacteristic
335C23×C1092−1+411yescharacteristic
336C23×C1092−1+411yescharacteristic
337C23×C1092−1+411yescharacteristic
338C23×C1092−1+411yescharacteristic
339C2×C4×C109—22no—
340C2×C4×C109—22no—
341C2×C4×C109—22no—
342C2×C4×C109—22no—
343C2×C4×C109—22no—
344C2×C4×C109—22no—
345C2×C4×C109—22no—
346C2×C4×C109—22no—
347C2×C4×C109—22no—
348C2×C4×C109—22no—
349C2×C4×C109—22no—
350C2×C4×C109—22no—
351C2×C4×C109—22no—
352C2×C4×C109—22no—
353C2×C4×C109—22no—
354C2×C4×C109—22no—
355C2×C4×C109—22no—
356C2×C4×C109—22no—
357C2×C4×C109—22no—
358C2×C4×C109—22no—
359C2×C4×C109—22no—
360C2×C4×C109—22no—
361C2×C4×C109—22no—
362C2×C4×C109—22no—
363C2×C4×C109—22no—
364C2×C4×C109—22no—
365C2×C4×C109—22no—
366C2×C4×C109—22no—
367C2×C4×C109—22no—
368C2×C4×C109—22no—
369C2×C4×C109—22no—
370C2×C4×C109—22no—
371C2×C4×C109—22no—
372C2×C4×C109—22no—
373C2×C4×C109—22no—
374C2×C4×C109—22no—
375C2×C4×C109—22no—
376C2×C4×C109—22no—
377C2×C4×C109—22no—
378C2×C4×C109—22no—
379C2×C4×C109—22no—
380C2×C4×C109—22no—
381C2×C4×C109—416no—
382C2×C4×C109—41no—
383C2×C4×C109—41no—
384C2×C4×C109—41no—
385C2×C4×C109—41no—
386C2×C4×C109—41no—
387C2×C4×C109—41no—
388C2×C4×C109—41no—
389C2×C4×C109—41no—
390C2×C4×C109—41no—
391C2×C4×C109—41no—
392C2×C4×C109—41no—
393C2×C4×C109—41no—
394C2×C4×C109—41no—
395C2×C4×C109—41no—
396C2×C4×C109—41no—
397C2×C4×C109—41no—
398C2×C4×C109—41no—
399C2×C4×C109—41no—
400C2×C4×C109—41no—
401C2×C4×C109—41no—
402C2×C4×C109—41no—
403C2×C4×C109—41no—
404C2×C4×C109—41no—
405C2×C4×C109—41no—
406C2×C4×C109—41no—
407C2×C4×C109—41no—
408C2×C4×C109—41no—
409C2×C4×C109—41no—
410C2×C4×C109—41no—
411C2×C4×C109—41no—
412C2×C4×C109—41no—
413C2×C4×C109—41no—
414C2×C4×C109—41no—
415C2×C4×C109—41no—
416C2×C4×C109—41no—
417C2×C4×C109—41no—
418C2×C4×C109—41no—
419C2×C4×C109—41no—
420C2×C4×C109—41no—
421C2×C4×C109—41no—
422C2×C4×C109—41no—
423C2×C4×C109—41no—
424C2×C4×C109—41no—
425C2×C4×C109—41no—
426C2×C4×C109—41no—
427C2×C4×C109—41no—
428C2×C4×C109—41no—
429C2×C4×C109—41no—
430C2×C4×C109—41no—
431C2×C4×C109—41no—
432C2×C4×C109—41no—
433C2×C4×C109—41no—
434C2×C4×C109C2×C4⋊C414yes—
435C2×C4×C109C2×C4⋊C414yes—
436C2×C4×C109C4×D414yes—
437C2×C4×C109C4×D414yes—
438C22×C109—24no—
439C22×C109—24no—
440C22×C109—24no—
441C22×C109—42no—
442C22×C109—42no—
443C22×C109—42no—
444C22×C109—42no—
445C22×C109—42no—
446C22×C109—42no—
447C22×C109—42no—
448C22×C109—42no—
449C22×C109—42no—
450C22×C109—42no—
451C22×C109—42no—
452C22×C109—42no—
453C22×C109C22×C4⋊C411yescharacteristic
454C22×C109C2×C4×D411yescharacteristic
455C22×C109C2×C4×D411yescharacteristic
456C22×C109#52011yescharacteristic
457C22×C109#52011yescharacteristic
458C22×C109#52011yescharacteristic
459C22×C109#52011yescharacteristic
460C22×C109#53411yescharacteristic
461C22×C109#53511yescharacteristic
462C22×C109#53511yescharacteristic
463C22×C109#53611yescharacteristic
464C22×C109#53611yescharacteristic
465C22×C109#53611yescharacteristic
466C22×C109#53911yescharacteristic
467C22×C109#53911yescharacteristic
468C22×C109#54211yescharacteristic
469C22×C109#54211yescharacteristic
470C22×C109#54411yescharacteristic
471C22×C109#54411yescharacteristic
472C22×C109D4211yescharacteristic
473C22×C109D4211yescharacteristic
474C22×C109D4211yescharacteristic
475C22×C109#54711yescharacteristic
476C22×C109#54711yescharacteristic
477C22×C109#54711yescharacteristic
478C22×C109#54811yescharacteristic
479C22×C109D4×Q811yescharacteristic
480C22×C109D4×Q811yescharacteristic
481C22×C109#55311yescharacteristic
482C22×C109#55411yescharacteristic
483C22×C109#55411yescharacteristic
484C22×C109#56011yescharacteristic
485C22×C109#56311yescharacteristic
486C22×C109#56311yescharacteristic
487C22×C109#56311yescharacteristic
488C4×C109—24no—
489C4×C109—24no—
490C4×C109—24no—
491C4×C109—24no—
492C4×C109—42no—
493C4×C109—42no—
494C4×C109—42no—
495C4×C109—42no—
496C4×C109—42no—
497C4×C109—42no—
498C4×C109—81no—
499C4×C109—81no—
500C4×C109—81no—
501C4×C109—81no—
502#14405C10911yesmaximal, characteristic, direct product factor, Sylow
503C2×C109—44no—
504C2×C109#231711yescharacteristic
505C2×C109#232211yescharacteristic
506C2×C109#232611yescharacteristic
507C2×C109D4×C4⋊C411yescharacteristic
508C2×C109D4×C4⋊C411yescharacteristic
509C2×C109#236111yescharacteristic
510C2×C109#238311yescharacteristic
511C2×C109#266911yescharacteristic
512C2×C109#267411yescharacteristic
513C2×C109#267711yescharacteristic
514C2×C109#268011yescharacteristic
515C2×C109#271811yescharacteristic
516C2×C109#272011yescharacteristic
517C2×C109#272911yescharacteristic
518C2×C109#279011yescharacteristic
519C2×#389C2×C10911yescharacteristic, complemented
520C2×#388C2×C10911yescharacteristic
521C2×#388C2×C10911yescharacteristic
522C2×#385C2×C10911yescharacteristic
523C2×#385C2×C10911yescharacteristic
524C2×#385C2×C10911yescharacteristic
525C2×#384C2×C10911yescharacteristic, complemented
526#1444C2×C10911yescharacteristic, complemented
527#1444C2×C10911yescharacteristic, complemented
528#1442C2×C10911yescharacteristic, complemented
529#1441C2×C10911yescharacteristic, complemented
530#1439C2×C10911yescharacteristic
531#1439C2×C10911yescharacteristic
532#1436C2×C10911yescharacteristic, complemented
533#1434C2×C10911yescharacteristic, complemented
534C109#1440511yescharacteristic, direct product factor, Sylow
535C24×C4C22×C10911yescharacteristic
536C22×C4⋊C4C22×C10911yescharacteristic
537C22×C4⋊C4C22×C10911yescharacteristic
538C22×C4⋊C4C22×C10911yescharacteristic
539C22×C4⋊C4C22×C10911yescharacteristic
540C22×C4⋊C4C22×C10911yescharacteristic
541C22×C4⋊C4C22×C10911yescharacteristic
542C22×C4⋊C4C22×C10911yescharacteristic
543C22×C4⋊C4C22×C10911yescharacteristic
544C22×C4⋊C4C22×C10911yescharacteristic
545C22×C4⋊C4C22×C10911yescharacteristic
546C22×C22⋊C4C22×C10911yescharacteristic
547C22×C22⋊C4C22×C10911yescharacteristic
548C22×C22⋊C4C22×C10911yescharacteristic
549C22×C22⋊C4C22×C10911yescharacteristic
550C22×C22⋊C4C22×C10911yescharacteristic
551C22×C22⋊C4C22×C10911yescharacteristic
552C22×C42C22×C10911yescharacteristic
553C22×C42C22×C10911yescharacteristic
554#389—24no—
555#388—24no—
556#388C4×C10918yescomplemented
557#385—24no—
558#385—24no—
559#385—24no—
560#384—24no—
561C2×#95C22×C10911yescharacteristic
562C2×#95C22×C10911yescharacteristic
563C2×#95C22×C10911yescharacteristic
564C2×#95C22×C10911yescharacteristic
565C2×#95C22×C10911yescharacteristic
566C2×#95C22×C10911yescharacteristic
567C2×#95C22×C10911yescharacteristic
568C2×#95C22×C10911yescharacteristic
569C2×#95C22×C10911yescharacteristic
570C2×#95C22×C10911yescharacteristic
571C2×#95C22×C10911yescharacteristic
572C2×#95C22×C10911yescharacteristic
573C2×#95C22×C10911yescharacteristic
574C2×#95C22×C10911yescharacteristic
575C2×#95C22×C10911yescharacteristic
576C2×#95C22×C10911yescharacteristic
577C25C23×C10911yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C10911yescharacteristic
586C23×C4C23×C10911yescharacteristic
587C23×C4C23×C10911yescharacteristic
588C23×C4C23×C10911yescharacteristic
589C23×C4C23×C10911yescharacteristic
590C23×C4C23×C10911yescharacteristic
591C23×C4C23×C10911yescharacteristic
592C23×C4C23×C10911yescharacteristic
593C23×C4C23×C10911yescharacteristic
594C23×C4C23×C10911yescharacteristic
595C23×C4C23×C10911yescharacteristic
596C23×C4C23×C10911yescharacteristic
597C23×C4C23×C10911yescharacteristic
598C23×C4C23×C10911yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×C4×C10914yescomplemented
628C2×C4⋊C4D4×C10914yes—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4C2×C4×C10914yes—
643C2×C22⋊C4C2×C4×C10914yes—
644C2×C22⋊C4C2×C4×C10914yes—
645C2×C22⋊C4D4×C10914yes—
646C2×C22⋊C4Q8×C10914yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—22no—
651C2×C42—41no—
652C2×C42C2×C4×C10914yescomplemented
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—41no—
664#95—41no—
665#95—41no—
666#95C2×C4×C10914yescomplemented
667#95C2×C4×C10914yescomplemented
668#95D4×C10914yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C10912yes—
682C24C2×D4×C10912yes—
683C24C2×Q8×C10912yes—
684C24C24×C10911yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C22×C4×C10912yes—
773C22×C4C22×C4×C10912yes—
774C22×C4C22×C4×C10912yes—
775C22×C4C22×C4×C10912yes—
776C22×C4C22×C4×C10912yes—
777C22×C4C22×C4×C10912yes—
778C22×C4C2×D4×C10912yes—
779C22×C4C2×D4×C10912yes—
780C22×C4C2×D4×C10912yes—
781C22×C4C2×D4×C10912yes—
782C22×C4C2×D4×C10912yes—
783C22×C4C2×D4×C10912yes—
784C22×C4C2×D4×C10912yes—
785C22×C4C2×D4×C10912yes—
786C22×C4C2×Q8×C10912yes—
787C22×C4C2×Q8×C10912yes—
788C22×C4#41×C10912yes—
789C22×C4#41×C10912yes—
790C4⋊C4—28no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4C4⋊C4×C109116yescomplemented
806C42—28no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C10914yes—
843C23C23×C4×C10911yescharacteristic
844C23C22×D4×C10911yescharacteristic
845C23C22×D4×C10911yescharacteristic
846C23C22×D4×C10911yescharacteristic
847C23C22×Q8×C10911yescharacteristic
848C23C2×#41×C10911yescharacteristic
849C23C2×#41×C10911yescharacteristic
850C23H(5,𝔽2)×C10911yescharacteristic
851C23H(5,𝔽2)×C10911yescharacteristic
852C23H(5,𝔽2)×C10911yescharacteristic
853C23H(5,𝔽2)×C10911yescharacteristic
854C232−1+4×C10911yescharacteristic
855C232−1+4×C10911yescharacteristic
856C232−1+4×C10911yescharacteristic
857C232−1+4×C10911yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—416no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4C2×C4⋊C4×C10914yes—
954C2×C4C2×C4⋊C4×C10914yes—
955C2×C4C4×D4×C10914yes—
956C2×C4C4×D4×C10914yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C10911yescharacteristic
973C22C2×C4×D4×C10911yescharacteristic
974C22C2×C4×D4×C10911yescharacteristic
975C22#520×C10911yescharacteristic
976C22#520×C10911yescharacteristic
977C22#520×C10911yescharacteristic
978C22#520×C10911yescharacteristic
979C22#534×C10911yescharacteristic
980C22#535×C10911yescharacteristic
981C22#535×C10911yescharacteristic
982C22#536×C10911yescharacteristic
983C22#536×C10911yescharacteristic
984C22#536×C10911yescharacteristic
985C22#539×C10911yescharacteristic
986C22#539×C10911yescharacteristic
987C22#542×C10911yescharacteristic
988C22#542×C10911yescharacteristic
989C22#544×C10911yescharacteristic
990C22#544×C10911yescharacteristic
991C22D42×C10911yescharacteristic
992C22D42×C10911yescharacteristic
993C22D42×C10911yescharacteristic
994C22#547×C10911yescharacteristic
995C22#547×C10911yescharacteristic
996C22#547×C10911yescharacteristic
997C22#548×C10911yescharacteristic
998C22D4×Q8×C10911yescharacteristic
999C22D4×Q8×C10911yescharacteristic
1000C22#553×C10911yescharacteristic
1001C22#554×C10911yescharacteristic
1002C22#554×C10911yescharacteristic
1003C22#560×C10911yescharacteristic
1004C22#563×C10911yescharacteristic
1005C22#563×C10911yescharacteristic
1006C22#563×C10911yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C109×#231711yescharacteristic
1023C2C109×#232211yescharacteristic
1024C2C109×#232611yescharacteristic
1025C2D4×C4⋊C4×C10911yescharacteristic
1026C2D4×C4⋊C4×C10911yescharacteristic
1027C2C109×#236111yescharacteristic
1028C2C109×#238311yescharacteristic
1029C2C109×#266911yescharacteristic
1030C2C109×#267411yescharacteristic
1031C2C109×#267711yescharacteristic
1032C2C109×#268011yescharacteristic
1033C2C109×#271811yescharacteristic
1034C2C109×#272011yescharacteristic
1035C2C109×#272911yescharacteristic
1036C2C109×#279011yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutatorC23C23×C4×C109
Frattini, cosocleC24C24×C109
prime radicalC25×C109C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C109C2semidirect
7. C2×#384×C109C2semidirect
8. C109×#1444C2semidirect
9. C109×#1444C2semidirect
10. C109×#1442C2semidirect
11. C109×#1441C2semidirect
14. C109×#1436C2semidirect
15. C109×#1434C2semidirect
37. #388×C109C4semidirect
108. C2×C4⋊C4×C109C2×C4semidirect
133. C2×C42×C109C2×C4semidirect
147. #95×C109C2×C4semidirect
148. #95×C109C2×C4semidirect
286. C22⋊C4×C109C4⋊C4semidirect
502. #14405C109direct (N × H)
519. C2×#389C2×C109semidirect
525. C2×#384C2×C109semidirect
526. #1444C2×C109semidirect
527. #1444C2×C109semidirect
528. #1442C2×C109semidirect
529. #1441C2×C109semidirect
532. #1436C2×C109semidirect
533. #1434C2×C109semidirect
534. C109#14405direct (N × H)
556. #388C4×C109semidirect
627. C2×C4⋊C4C2×C4×C109semidirect
652. C2×C42C2×C4×C109semidirect
666. #95C2×C4×C109semidirect
667. #95C2×C4×C109semidirect
805. C22⋊C4C4⋊C4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1092
C2×#388×C1092
C2×#385×C1092
C2×#384×C1092
C109×#14442
C109×#14422
C109×#14412
C109×#14392
C109×#14362
C109×#14342
#14405109