Finite Group Databasebeta

← C109×#24053 #42142047

Subgroups — C109×#24053 #42142047

Order 27904.

1284 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C109C211yesmaximal, characteristic
2C2×#485×C109C211yesmaximal, characteristic, complemented
3C2×#419×C109C211yesmaximal, characteristic, complemented
4C109×#2485C211yesmaximal, characteristic
5C109×#2043C211yesmaximal, characteristic, complemented
6C109×#2043C211yesmaximal, characteristic, complemented
7C109×#2036C211yesmaximal, characteristic, complemented
8C109×#2035C211yesmaximal, characteristic, complemented
9C109×#1894C211yesmaximal, characteristic, complemented
10C109×#1870C211yesmaximal, characteristic
11C109×#1865C211yesmaximal, characteristic, complemented
12C109×#1863C211yesmaximal, characteristic, complemented
13C109×#1787C211yesmaximal, characteristic, complemented
14C109×#1787C211yesmaximal, characteristic, complemented
15C109×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C109C2211yescharacteristic
17C23×Q8×C109C2211yescharacteristic
18C22×M16×C109C2211yescharacteristic
19D4×Q8×C109—24no—
20D4×Q8×C109—24no—
21C2×C4⋊Q8×C109—21no—
22C2×C4⋊Q8×C109C2211yescharacteristic
23C2×C22⋊Q8×C109—21no—
24C2×C22⋊Q8×C109—21no—
25C2×C22⋊Q8×C109C2211yescharacteristic
26C2×C22⋊Q8×C109C2211yescharacteristic
27C2×C4×Q8×C109C2211yescharacteristic
28C2×C4×D4×C109—21no—
29C2×C4×D4×C109C2211yescharacteristic
30C2×#117×C109C2211yescharacteristic
31#485×C109—24no—
32C2×#107×C109C2211yescharacteristic
33C2×#106×C109C2211yescharacteristic
34#419×C109—24no—
35C2×#103×C109C2211yescharacteristic
36C2×#103×C109C2211yescharacteristic
37C2×#103×C109C2211yescharacteristic
38C2×#103×C109C2211yescharacteristic
39C2×#103×C109C2211yescharacteristic
40C2×#103×C109C2211yescharacteristic
41C2×#103×C109C2211yescharacteristic
42C2×#103×C109C2211yescharacteristic
43C2×#103×C109C2211yescharacteristic
44C2×#103×C109C2211yescharacteristic
45C2×#103×C109C2211yescharacteristic
46C2×#103×C109C2211yescharacteristic
47C2×C22⋊C8×C109C2211yescharacteristic
48C2×C22⋊C8×C109C2211yescharacteristic
49C2×C22⋊C8×C109C2211yescharacteristic
50#397×C109—21no—
51#394×C109—21no—
52#389×C109C2211yescharacteristic
53#389×C109C2211yescharacteristic
54#388×C109—21no—
55#387×C109—21no—
56#380×C109C2211yescharacteristic
57#380×C109C2211yescharacteristic
58#380×C109C2211yescharacteristic
59#340×C109C2211yescharacteristic
60#340×C109C2211yescharacteristic
61#336×C109C2211yescharacteristic
62#336×C109C2211yescharacteristic
63C22×Q8×C109—22no—
64C22×Q8×C109—22no—
65C22×Q8×C109—21no—
66C22×Q8×C109—21no—
67C22×Q8×C109—22no—
68C22×Q8×C109—22no—
69C22×Q8×C109—22no—
70C22×Q8×C109—22no—
71C22×Q8×C109—22no—
72C22×Q8×C109—41no—
73C22×Q8×C109—41no—
74C22×Q8×C109—41no—
75C22×Q8×C109—41no—
76C22×Q8×C109D414yes—
77C22×Q8×C109C2311yescharacteristic
78C22×Q8×C109C2311yescharacteristic
79C22×Q8×C109C2311yescharacteristic
80C22×D4×C109D411yescharacteristic
81C23×C4×C109—21no—
82C23×C4×C109—21no—
83C23×C4×C109C2311yescharacteristic
84C23×C4×C109C2311yescharacteristic
85C2×M16×C109—22no—
86C2×M16×C109—41no—
87C2×M16×C109—41no—
88C22×C8×C109C2311yescharacteristic
89C22×C8×C109C2311yescharacteristic
90C22×C8×C109C2311yescharacteristic
91C22×C8×C109C2311yescharacteristic
92C4⋊Q8×C109—28no—
93C4⋊Q8×C109—22no—
94C4⋊Q8×C109—22no—
95C22⋊Q8×C109—28no—
96C22⋊Q8×C109—28no—
97C22⋊Q8×C109—22no—
98C22⋊Q8×C109—22no—
99C22⋊Q8×C109—22no—
100C22⋊Q8×C109D414yes—
101C4×Q8×C109—22no—
102C4×Q8×C109—22no—
103C4×D4×C109—28no—
104C4×D4×C109—22no—
105C4×D4×C109—22no—
106#117×C109—22no—
107#117×C109—22no—
108C2×C4⋊C4×C109—21no—
109C2×C4⋊C4×C109—21no—
110C2×C4⋊C4×C109—21no—
111C2×C4⋊C4×C109—21no—
112C2×C4⋊C4×C109—21no—
113C2×C4⋊C4×C109—21no—
114C2×C4⋊C4×C109—21no—
115C2×C4⋊C4×C109D411yescharacteristic
116C2×C4⋊C4×C109C2311yescharacteristic
117C2×C4⋊C4×C109C2311yescharacteristic
118C2×C4⋊C4×C109C2311yescharacteristic
119C2×C4⋊C4×C109C2311yescharacteristic
120C2×C4⋊C4×C109C2311yescharacteristic
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109D411yescharacteristic
128C2×C22⋊C4×C109D411yescharacteristic
129C2×C42×C109—21no—
130C2×C42×C109—21no—
131C2×C42×C109C2311yescharacteristic
132#107×C109—22no—
133#106×C109—22no—
134#103×C109—22no—
135#103×C109—22no—
136#103×C109—22no—
137#103×C109—22no—
138#103×C109—22no—
139#103×C109—22no—
140#103×C109—22no—
141#103×C109—22no—
142#103×C109—41no—
143#103×C109—41no—
144#103×C109—41no—
145#103×C109—41no—
146C22⋊C8×C109—22no—
147C22⋊C8×C109—41no—
148C22⋊C8×C109—41no—
149#95×C109—21no—
150#95×C109—21no—
151#95×C109—21no—
152#95×C109—21no—
153#95×C109—21no—
154C24×C109C2×D411yescharacteristic
155C24×C109C2×D411yescharacteristic
156C2×Q8×C109—24no—
157C2×Q8×C109—24no—
158C2×Q8×C109—21no—
159C2×Q8×C109—21no—
160C2×Q8×C109—21no—
161C2×Q8×C109—21no—
162C2×Q8×C109—21no—
163C2×Q8×C109—28no—
164C2×Q8×C109—21no—
165C2×Q8×C109—21no—
166C2×Q8×C109—21no—
167C2×Q8×C109—21no—
168C2×Q8×C109—21no—
169C2×Q8×C109—21no—
170C2×Q8×C109—21no—
171C2×Q8×C109—21no—
172C2×Q8×C109—42no—
173C2×Q8×C109—42no—
174C2×Q8×C109—42no—
175C2×Q8×C109—42no—
176C2×Q8×C109—44no—
177C2×Q8×C109—44no—
178C2×Q8×C109—44no—
179C2×Q8×C109—44no—
180C2×Q8×C109—44no—
181C2×Q8×C109—44no—
182C2×Q8×C109—44no—
183C2×Q8×C109C2×D412yes—
184C2×Q8×C109C2×D412yes—
185C2×Q8×C109C2×D412yes—
186C2×Q8×C109#4112yes—
187C2×Q8×C109#4112yes—
188C2×D4×C109—22no—
189C2×D4×C109—22no—
190C2×D4×C109—22no—
191C22×C4×C109—21no—
192C22×C4×C109—21no—
193C22×C4×C109—21no—
194C22×C4×C109—21no—
195C22×C4×C109—21no—
196C22×C4×C109—24no—
197C22×C4×C109—24no—
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—42no—
212C22×C4×C109—42no—
213C22×C4×C109—42no—
214C22×C4×C109—42no—
215C22×C4×C109C2×D411yescharacteristic
216C22×C4×C109C2×D411yescharacteristic
217C22×C4×C109C2×D411yescharacteristic
218C22×C4×C109C2×D412yes—
219C22×C4×C109C2×D412yes—
220C22×C4×C109C2×D411yescharacteristic
221C22×C4×C109C2411yescharacteristic
222M16×C109—44no—
223C2×C8×C109—21no—
224C2×C8×C109—21no—
225C2×C8×C109—21no—
226C2×C8×C109—21no—
227C2×C8×C109—21no—
228C2×C8×C109—21no—
229C2×C8×C109—21no—
230C2×C8×C109—21no—
231C2×C8×C109—21no—
232C2×C8×C109—21no—
233C2×C8×C109—21no—
234C2×C8×C109—21no—
235C4⋊C4×C109—24no—
236C4⋊C4×C109—24no—
237C4⋊C4×C109—24no—
238C4⋊C4×C109—24no—
239C4⋊C4×C109—24no—
240C4⋊C4×C109—22no—
241C4⋊C4×C109—21no—
242C4⋊C4×C109—21no—
243C4⋊C4×C109—21no—
244C4⋊C4×C109—21no—
245C4⋊C4×C109—21no—
246C4⋊C4×C109—21no—
247C4⋊C4×C109—21no—
248C4⋊C4×C109—21no—
249C4⋊C4×C109—21no—
250C4⋊C4×C109—42no—
251C4⋊C4×C109—81no—
252C4⋊C4×C109C2×D412yes—
253C22⋊C4×C109—24no—
254C22⋊C4×C109—24no—
255C22⋊C4×C109—22no—
256C22⋊C4×C109—22no—
257C22⋊C4×C109—42no—
258C22⋊C4×C109—42no—
259C22⋊C4×C109—81no—
260C22⋊C4×C109—81no—
261C42×C109—24no—
262C42×C109—21no—
263C42×C109—21no—
264C42×C109—42no—
265C23×C109—21no—
266C23×C109—21no—
267C23×C109—21no—
268C23×C109—21no—
269C23×C109—21no—
270C23×C109—21no—
271C23×C109—21no—
272C23×C109—21no—
273C23×C109—21no—
274C23×C109—21no—
275C23×C109—21no—
276C23×C109—21no—
277C23×C109#12012yes—
278C23×C109#13712yes—
279C23×C109C22×D411yescharacteristic
280Q8×C109—22no—
281Q8×C109—22no—
282Q8×C109—22no—
283Q8×C109—22no—
284Q8×C109—22no—
285Q8×C109—22no—
286Q8×C109—22no—
287Q8×C109—48no—
288Q8×C109—48no—
289Q8×C109—41no—
290Q8×C109—41no—
291Q8×C109—41no—
292Q8×C109—41no—
293Q8×C109#12314yes—
294D4×C109—28no—
295C2×C4×C109—21no—
296C2×C4×C109—22no—
297C2×C4×C109—21no—
298C2×C4×C109—21no—
299C2×C4×C109—22no—
300C2×C4×C109—22no—
301C2×C4×C109—21no—
302C2×C4×C109—22no—
303C2×C4×C109—22no—
304C2×C4×C109—22no—
305C2×C4×C109—22no—
306C2×C4×C109—21no—
307C2×C4×C109—22no—
308C2×C4×C109—22no—
309C2×C4×C109—22no—
310C2×C4×C109—21no—
311C2×C4×C109—21no—
312C2×C4×C109—21no—
313C2×C4×C109—21no—
314C2×C4×C109—21no—
315C2×C4×C109—48no—
316C2×C4×C109—48no—
317C2×C4×C109—41no—
318C2×C4×C109—41no—
319C2×C4×C109—41no—
320C2×C4×C109—41no—
321C2×C4×C109—41no—
322C2×C4×C109—41no—
323C2×C4×C109—41no—
324C2×C4×C109—41no—
325C2×C4×C109—41no—
326C2×C4×C109—41no—
327C2×C4×C109—41no—
328C2×C4×C109—41no—
329C2×C4×C109—41no—
330C2×C4×C109—41no—
331C2×C4×C109—41no—
332C2×C4×C109—41no—
333C2×C4×C109—41no—
334C2×C4×C109—41no—
335C2×C4×C109—41no—
336C2×C4×C109—41no—
337C2×C4×C109—41no—
338C2×C4×C109—41no—
339C2×C4×C109#12012yes—
340C2×C4×C109#13712yes—
341C2×C4×C109C22×D411yescharacteristic
342C2×C4×C109C22×D411yescharacteristic
343C2×C4×C109C2×#4111yescharacteristic
344C2×C4×C109C2×#4111yescharacteristic
345C2×C4×C109H(5,𝔽2)11yescharacteristic
346C2×C4×C109H(5,𝔽2)11yescharacteristic
347C8×C109—41no—
348C8×C109—41no—
349C8×C109—41no—
350C8×C109—41no—
351C22×C109—22no—
352C22×C109—22no—
353C22×C109—22no—
354C22×C109—22no—
355C22×C109—22no—
356C22×C109—22no—
357C22×C109—41no—
358C22×C109—41no—
359C22×C109—41no—
360C22×C109—41no—
361C22×C109—41no—
362C22×C109—41no—
363C22×C109—41no—
364C22×C109—41no—
365C22×C109C2×#12011yescharacteristic
366C22×C109#54611yescharacteristic
367C22×C109#54611yescharacteristic
368C22×C109C2×#13711yescharacteristic
369C22×C109C2×#13711yescharacteristic
370C22×C109#57711yescharacteristic
371C22×C109#57811yescharacteristic
372C4×C109—22no—
373C4×C109—24no—
374C4×C109—22no—
375C4×C109—41no—
376C4×C109—42no—
377C4×C109—42no—
378C4×C109—41no—
379C4×C109—42no—
380C4×C109—81no—
381C4×C109—81no—
382C4×C109—81no—
383C4×C109—81no—
384C4×C109C2×#12311yescharacteristic
385C4×C109#53411yescharacteristic
386C4×C109#54611yescharacteristic
387C4×C109#54611yescharacteristic
388#24053C10911yesmaximal, characteristic, direct product factor, Sylow
389C2×C109—42no—
390C2×C109—42no—
391C2×C109#240511yescharacteristic
392C2×C109#300411yescharacteristic
393C2×C109#301311yescharacteristic
394C2×C109#331211yescharacteristic
395C2×C109#332011yescharacteristic
396C2×C109#332811yescharacteristic
397C2×C109#332911yescharacteristic
398C2×D4×Q8C2×C10911yescharacteristic
399C2×#485C2×C10911yescharacteristic, complemented
400C2×#419C2×C10911yescharacteristic, complemented
401#2485C2×C10911yescharacteristic
402#2043C2×C10911yescharacteristic, complemented
403#2043C2×C10911yescharacteristic, complemented
404#2036C2×C10911yescharacteristic, complemented
405#2035C2×C10911yescharacteristic, complemented
406#1894C2×C10911yescharacteristic, complemented
407#1870C2×C10911yescharacteristic
408#1865C2×C10911yescharacteristic, complemented
409#1863C2×C10911yescharacteristic, complemented
410#1787C2×C10911yescharacteristic, complemented
411#1787C2×C10911yescharacteristic, complemented
412#1787C2×C10911yescharacteristic, complemented
413C109#2405311yescharacteristic, direct product factor, Sylow
414C23×Q8C22×C10911yescharacteristic
415C23×Q8C22×C10911yescharacteristic
416C22×M16C22×C10911yescharacteristic
417D4×Q8—24no—
418D4×Q8—24no—
419C2×C4⋊Q8—21no—
420C2×C4⋊Q8C22×C10911yescharacteristic
421C2×C22⋊Q8—21no—
422C2×C22⋊Q8—21no—
423C2×C22⋊Q8C22×C10911yescharacteristic
424C2×C22⋊Q8C22×C10911yescharacteristic
425C2×C4×Q8C22×C10911yescharacteristic
426C2×C4×D4—21no—
427C2×C4×D4C22×C10911yescharacteristic
428C2×#117C22×C10911yescharacteristic
429#485—24no—
430C2×#107C22×C10911yescharacteristic
431C2×#106C22×C10911yescharacteristic
432#419—24no—
433C2×#103C22×C10911yescharacteristic
434C2×#103C22×C10911yescharacteristic
435C2×#103C22×C10911yescharacteristic
436C2×#103C22×C10911yescharacteristic
437C2×#103C22×C10911yescharacteristic
438C2×#103C22×C10911yescharacteristic
439C2×#103C22×C10911yescharacteristic
440C2×#103C22×C10911yescharacteristic
441C2×#103C22×C10911yescharacteristic
442C2×#103C22×C10911yescharacteristic
443C2×#103C22×C10911yescharacteristic
444C2×#103C22×C10911yescharacteristic
445C2×C22⋊C8C22×C10911yescharacteristic
446C2×C22⋊C8C22×C10911yescharacteristic
447C2×C22⋊C8C22×C10911yescharacteristic
448#397—21no—
449#394—21no—
450#389C22×C10911yescharacteristic
451#389C22×C10911yescharacteristic
452#388—21no—
453#387—21no—
454#380C22×C10911yescharacteristic
455#380C22×C10911yescharacteristic
456#380C22×C10911yescharacteristic
457#340C22×C10911yescharacteristic
458#340C22×C10911yescharacteristic
459#336C22×C10911yescharacteristic
460#336C22×C10911yescharacteristic
461C22×Q8—22no—
462C22×Q8—22no—
463C22×Q8—21no—
464C22×Q8—21no—
465C22×Q8—22no—
466C22×Q8—22no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—22no—
470C22×Q8—41no—
471C22×Q8—41no—
472C22×Q8—41no—
473C22×Q8—41no—
474C22×Q8D4×C10914yes—
475C22×Q8C23×C10911yescharacteristic
476C22×Q8C23×C10911yescharacteristic
477C22×Q8C23×C10911yescharacteristic
478C22×D4D4×C10911yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C10911yescharacteristic
482C23×C4C23×C10911yescharacteristic
483C2×M16—22no—
484C2×M16—41no—
485C2×M16—41no—
486C22×C8C23×C10911yescharacteristic
487C22×C8C23×C10911yescharacteristic
488C22×C8C23×C10911yescharacteristic
489C22×C8C23×C10911yescharacteristic
490C4⋊Q8—28no—
491C4⋊Q8—22no—
492C4⋊Q8—22no—
493C22⋊Q8—28no—
494C22⋊Q8—28no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8D4×C10914yes—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×D4—28no—
502C4×D4—22no—
503C4×D4—22no—
504#117—22no—
505#117—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4D4×C10911yescharacteristic
514C2×C4⋊C4C23×C10911yescharacteristic
515C2×C4⋊C4C23×C10911yescharacteristic
516C2×C4⋊C4C23×C10911yescharacteristic
517C2×C4⋊C4C23×C10911yescharacteristic
518C2×C4⋊C4C23×C10911yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4D4×C10911yescharacteristic
526C2×C22⋊C4D4×C10911yescharacteristic
527C2×C42—21no—
528C2×C42—21no—
529C2×C42C23×C10911yescharacteristic
530#107—22no—
531#106—22no—
532#103—22no—
533#103—22no—
534#103—22no—
535#103—22no—
536#103—22no—
537#103—22no—
538#103—22no—
539#103—22no—
540#103—41no—
541#103—41no—
542#103—41no—
543#103—41no—
544C22⋊C8—22no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552C24C2×D4×C10911yescharacteristic
553C24C2×D4×C10911yescharacteristic
554C2×Q8—24no—
555C2×Q8—24no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—28no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—44no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8C2×D4×C10912yes—
582C2×Q8C2×D4×C10912yes—
583C2×Q8C2×D4×C10912yes—
584C2×Q8#41×C10912yes—
585C2×Q8#41×C10912yes—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4C2×D4×C10911yescharacteristic
614C22×C4C2×D4×C10911yescharacteristic
615C22×C4C2×D4×C10911yescharacteristic
616C22×C4C2×D4×C10912yes—
617C22×C4C2×D4×C10912yes—
618C22×C4C2×D4×C10911yescharacteristic
619C22×C4C24×C10911yescharacteristic
620M16—44no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—81no—
650C4⋊C4C2×D4×C10912yes—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—42no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23#120×C10912yes—
676C23#137×C10912yes—
677C23C22×D4×C10911yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—48no—
686Q8—48no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8#123×C10914yes—
692D4—28no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—48no—
714C2×C4—48no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4#120×C10912yes—
738C2×C4#137×C10912yes—
739C2×C4C22×D4×C10911yescharacteristic
740C2×C4C22×D4×C10911yescharacteristic
741C2×C4C2×#41×C10911yescharacteristic
742C2×C4C2×#41×C10911yescharacteristic
743C2×C4H(5,𝔽2)×C10911yescharacteristic
744C2×C4H(5,𝔽2)×C10911yescharacteristic
745C8—41no—
746C8—41no—
747C8—41no—
748C8—41no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22C2×#120×C10911yescharacteristic
764C22#546×C10911yescharacteristic
765C22#546×C10911yescharacteristic
766C22C2×#137×C10911yescharacteristic
767C22C2×#137×C10911yescharacteristic
768C22#577×C10911yescharacteristic
769C22#578×C10911yescharacteristic
770C4—22no—
771C4—22no—
772C4—24no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4C2×#123×C10911yescharacteristic
783C4#534×C10911yescharacteristic
784C4#546×C10911yescharacteristic
785C4#546×C10911yescharacteristic
786C2—42no—
787C2—42no—
788C2C109×#240511yescharacteristic
789C2C109×#300411yescharacteristic
790C2C109×#301311yescharacteristic
791C2C109×#331211yescharacteristic
792C2C109×#332011yescharacteristic
793C2C109×#332811yescharacteristic
794C2C109×#332911yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC22×D4×C109D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C109C2semidirect
3. C2×#419×C109C2semidirect
5. C109×#2043C2semidirect
6. C109×#2043C2semidirect
7. C109×#2036C2semidirect
8. C109×#2035C2semidirect
9. C109×#1894C2semidirect
11. C109×#1865C2semidirect
12. C109×#1863C2semidirect
13. C109×#1787C2semidirect
14. C109×#1787C2semidirect
15. C109×#1787C2semidirect
388. #24053C109direct (N × H)
399. C2×#485C2×C109semidirect
400. C2×#419C2×C109semidirect
402. #2043C2×C109semidirect
403. #2043C2×C109semidirect
404. #2036C2×C109semidirect
405. #2035C2×C109semidirect
406. #1894C2×C109semidirect
408. #1865C2×C109semidirect
409. #1863C2×C109semidirect
410. #1787C2×C109semidirect
411. #1787C2×C109semidirect
412. #1787C2×C109semidirect
413. C109#24053direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1092
C2×#485×C1092
C2×#419×C1092
C109×#24852
C109×#20432
C109×#20362
C109×#20352
C109×#18942
C109×#18702
C109×#18652
C109×#18632
C109×#17872
#24053109