Finite Group Databasebeta

← C109×#32730 #42150724

Subgroups — C109×#32730 #42150724

Order 27904.

824 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2624C211yesmaximal, characteristic, complemented
2C109×#2619C211yesmaximal, characteristic, complemented
3C109×#2101C211yesmaximal, characteristic, complemented
4C109×#2092C211yesmaximal, characteristic, complemented
5C109×#2067C211yesmaximal, characteristic, complemented
6C109×#2065C211yesmaximal, characteristic, complemented
7C109×#2054C211yesmaximal, characteristic, complemented
8C109×#2054C211yesmaximal, characteristic, complemented
9C109×#2041C211yesmaximal, characteristic, complemented
10C109×#2034C211yesmaximal, characteristic, complemented
11C109×#2033C211yesmaximal, characteristic, complemented
12C109×#2011C211yesmaximal, characteristic, complemented
13C109×#1999C211yesmaximal, characteristic, complemented
14C109×#1999C211yesmaximal, characteristic, complemented
15C109×#1798C211yesmaximal, characteristic, complemented
16C22×D8×C109C2211yescharacteristic
17C22×D8×C109C2211yescharacteristic
18C2×#127×C109C2211yescharacteristic
19C2×#121×C109C2211yescharacteristic
20C2×#121×C109C2211yescharacteristic
21C2×#121×C109C2211yescharacteristic
22C2×#117×C109C2211yescharacteristic
23C2×#107×C109C2211yescharacteristic
24C2×#106×C109C2211yescharacteristic
25C2×C4⋊C8×C109C2211yescharacteristic
26C2×C4⋊C8×C109C2211yescharacteristic
27C2×#102×C109C2211yescharacteristic
28C2×#102×C109C2211yescharacteristic
29C2×#102×C109C2211yescharacteristic
30C2×#102×C109C2211yescharacteristic
31C2×#102×C109C2211yescharacteristic
32C2×#102×C109C2211yescharacteristic
33C2×#102×C109C2211yescharacteristic
34C2×#102×C109C2211yescharacteristic
35C2×C22⋊C8×C109C2211yescharacteristic
36C2×C22⋊C8×C109C2211yescharacteristic
37#399×C109—21no—
38#397×C109—21no—
39#394×C109—21no—
40#394×C109—21no—
41#394×C109—21no—
42#394×C109—21no—
43#392×C109—21no—
44#392×C109—21no—
45#390×C109C2211yescharacteristic
46#390×C109C2211yescharacteristic
47#390×C109C2211yescharacteristic
48#390×C109C2211yescharacteristic
49#389×C109C2211yescharacteristic
50#389×C109C2211yescharacteristic
51#382×C109C2211yescharacteristic
52#380×C109C2211yescharacteristic
53#340×C109C2211yescharacteristic
54#340×C109C2211yescharacteristic
55#340×C109C2211yescharacteristic
56#340×C109C2211yescharacteristic
57#336×C109C2211yescharacteristic
58#336×C109C2211yescharacteristic
59C22×D4×C109—21no—
60C22×D4×C109—21no—
61C22×D4×C109—21no—
62C22×D4×C109—21no—
63C22×D4×C109—21no—
64C22×D4×C109C2311yescharacteristic
65C22×D4×C109C2311yescharacteristic
66C22×D4×C109C2311yescharacteristic
67C23×C4×C109C2311yescharacteristic
68C2×D8×C109—41no—
69C2×D8×C109—41no—
70C2×D8×C109—41no—
71C2×D8×C109—41no—
72C2×D8×C109—41no—
73C2×D8×C109—41no—
74C22×C8×C109C2311yescharacteristic
75C22×C8×C109C2311yescharacteristic
76C22×C8×C109C2311yescharacteristic
77C22×C8×C109C2311yescharacteristic
78#127×C109—41no—
79#127×C109—41no—
80#121×C109—41no—
81#121×C109—41no—
82#121×C109—41no—
83#121×C109—41no—
84#121×C109—41no—
85#121×C109—41no—
86#117×C109—41no—
87#117×C109—41no—
88C2×C4⋊C4×C109—21no—
89C2×C4⋊C4×C109—21no—
90C2×C4⋊C4×C109D411yescharacteristic
91C2×C4⋊C4×C109D411yescharacteristic
92C2×C4⋊C4×C109C2311yescharacteristic
93C2×C4⋊C4×C109C2311yescharacteristic
94C2×C4⋊C4×C109C2311yescharacteristic
95C2×C4⋊C4×C109C2311yescharacteristic
96C2×C4⋊C4×C109C2311yescharacteristic
97C2×C22⋊C4×C109—21no—
98C2×C22⋊C4×C109—21no—
99C2×C22⋊C4×C109—21no—
100C2×C22⋊C4×C109—21no—
101C2×C22⋊C4×C109—21no—
102C2×C22⋊C4×C109—21no—
103C2×C22⋊C4×C109—21no—
104C2×C22⋊C4×C109—21no—
105C2×C22⋊C4×C109—21no—
106C2×C22⋊C4×C109—21no—
107C2×C22⋊C4×C109—21no—
108C2×C22⋊C4×C109—21no—
109C2×C22⋊C4×C109D411yescharacteristic
110C2×C22⋊C4×C109D411yescharacteristic
111C2×C42×C109C2311yescharacteristic
112C2×C42×C109C2311yescharacteristic
113#107×C109—41no—
114#106×C109—41no—
115C4⋊C8×C109—41no—
116C4⋊C8×C109—41no—
117#102×C109—41no—
118#102×C109—41no—
119#102×C109—41no—
120#102×C109—41no—
121#102×C109—41no—
122#102×C109—41no—
123#102×C109—41no—
124#102×C109—41no—
125C22⋊C8×C109—41no—
126C22⋊C8×C109—41no—
127#95×C109—21no—
128#95×C109—21no—
129#95×C109—21no—
130#95×C109—21no—
131#95×C109—21no—
132C24×C109—21no—
133C24×C109—21no—
134C24×C109—21no—
135C24×C109C2×D411yescharacteristic
136C2×D4×C109—21no—
137C2×D4×C109—21no—
138C2×D4×C109—21no—
139C2×D4×C109—21no—
140C2×D4×C109—21no—
141C2×D4×C109—21no—
142C2×D4×C109—21no—
143C2×D4×C109—21no—
144C2×D4×C109—21no—
145C2×D4×C109—21no—
146C2×D4×C109—21no—
147C2×D4×C109—21no—
148C2×D4×C109—21no—
149C2×D4×C109—21no—
150C2×D4×C109—21no—
151C2×D4×C109—21no—
152C2×D4×C109—21no—
153C2×D4×C109—21no—
154C2×D4×C109—42no—
155C2×D4×C109—42no—
156C2×D4×C109—42no—
157C2×D4×C109—42no—
158C2×D4×C109—42no—
159C2×D4×C109—81no—
160C2×D4×C109—81no—
161C2×D4×C109—81no—
162C2×D4×C109—81no—
163C2×D4×C109—81no—
164C2×D4×C109—81no—
165C2×D4×C109—81no—
166C2×D4×C109—81no—
167C2×D4×C109—81no—
168C2×D4×C109—81no—
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×C109C2×D411yescharacteristic
181C22×C4×C109C2×D411yescharacteristic
182C22×C4×C109C2×D411yescharacteristic
183C22×C4×C109C2×D411yescharacteristic
184C22×C4×C109C2×D411yescharacteristic
185C22×C4×C109C2411yescharacteristic
186D8×C109—44no—
187D8×C109—44no—
188C2×C8×C109—21no—
189C2×C8×C109—21no—
190C2×C8×C109—21no—
191C2×C8×C109—21no—
192C2×C8×C109—21no—
193C2×C8×C109—21no—
194C2×C8×C109—21no—
195C2×C8×C109—21no—
196C2×C8×C109—21no—
197C2×C8×C109—21no—
198C2×C8×C109—21no—
199C2×C8×C109—21no—
200C4⋊C4×C109—21no—
201C4⋊C4×C109—21no—
202C4⋊C4×C109—21no—
203C4⋊C4×C109—21no—
204C4⋊C4×C109—21no—
205C4⋊C4×C109—21no—
206C4⋊C4×C109—21no—
207C4⋊C4×C109—21no—
208C4⋊C4×C109—21no—
209C4⋊C4×C109—21no—
210C4⋊C4×C109—41no—
211C4⋊C4×C109—41no—
212C4⋊C4×C109—81no—
213C4⋊C4×C109—81no—
214C22⋊C4×C109—41no—
215C22⋊C4×C109—41no—
216C22⋊C4×C109—42no—
217C22⋊C4×C109—42no—
218C22⋊C4×C109—42no—
219C22⋊C4×C109—81no—
220C22⋊C4×C109—81no—
221C22⋊C4×C109—81no—
222C22⋊C4×C109—81no—
223C22⋊C4×C109—81no—
224C22⋊C4×C109—81no—
225C22⋊C4×C109—81no—
226C22⋊C4×C109—81no—
227C22⋊C4×C109—81no—
228C42×C109—21no—
229C42×C109—21no—
230C42×C109—21no—
231C42×C109—21no—
232C23×C109—21no—
233C23×C109—21no—
234C23×C109—21no—
235C23×C109—21no—
236C23×C109—21no—
237C23×C109—21no—
238C23×C109—21no—
239C23×C109—41no—
240C23×C109—41no—
241C23×C109—41no—
242C23×C109—41no—
243C23×C109—41no—
244C23×C109—41no—
245C23×C109—41no—
246C23×C109—41no—
247C23×C109—41no—
248C23×C109—41no—
249C23×C109—41no—
250C23×C109—41no—
251C23×C109—41no—
252C23×C109—41no—
253C23×C109—41no—
254C23×C109—41no—
255C23×C109—41no—
256C23×C109—41no—
257C23×C109—41no—
258C23×C109—41no—
259C23×C109—41no—
260C23×C109C22×D411yescharacteristic
261D4×C109—41no—
262D4×C109—41no—
263D4×C109—41no—
264D4×C109—41no—
265D4×C109—41no—
266D4×C109—41no—
267D4×C109—41no—
268D4×C109—41no—
269D4×C109—41no—
270D4×C109—41no—
271D4×C109—41no—
272D4×C109—41no—
273D4×C109—84no—
274D4×C109—84no—
275D4×C109—84no—
276D4×C109—84no—
277D4×C109—84no—
278C2×C4×C109—21no—
279C2×C4×C109—21no—
280C2×C4×C109—21no—
281C2×C4×C109—21no—
282C2×C4×C109—21no—
283C2×C4×C109—21no—
284C2×C4×C109—21no—
285C2×C4×C109—21no—
286C2×C4×C109—21no—
287C2×C4×C109—21no—
288C2×C4×C109—21no—
289C2×C4×C109—21no—
290C2×C4×C109—21no—
291C2×C4×C109—21no—
292C2×C4×C109—21no—
293C2×C4×C109—41no—
294C2×C4×C109—41no—
295C2×C4×C109—41no—
296C2×C4×C109—41no—
297C2×C4×C109—41no—
298C2×C4×C109—41no—
299C2×C4×C109—41no—
300C2×C4×C109—41no—
301C2×C4×C109—41no—
302C2×C4×C109—41no—
303C2×C4×C109—41no—
304C2×C4×C109—41no—
305C2×C4×C109—41no—
306C2×C4×C109—41no—
307C2×C4×C109—41no—
308C2×C4×C109—41no—
309C2×C4×C109—41no—
310C2×C4×C109—41no—
311C2×C4×C109—41no—
312C2×C4×C109H(5,𝔽2)11yescharacteristic
313C2×C4×C109H(5,𝔽2)11yescharacteristic
314C2×C4×C109H(5,𝔽2)11yescharacteristic
315C2×C4×C109H(5,𝔽2)11yescharacteristic
316C2×C4×C109H(5,𝔽2)11yescharacteristic
317C2×C4×C1092−1+411yescharacteristic
318C8×C109—41no—
319C8×C109—41no—
320C8×C109—41no—
321C8×C109—41no—
322C22×C109—41no—
323C22×C109—41no—
324C22×C109—41no—
325C22×C109—41no—
326C22×C109—41no—
327C22×C109—41no—
328C22×C109—41no—
329C22×C109—81no—
330C22×C109—81no—
331C22×C109—81no—
332C22×C109—81no—
333C22×C109—81no—
334C22×C109—81no—
335C22×C109—81no—
336C22×C109—81no—
337C22×C109—81no—
338C22×C109—81no—
339C22×C109—81no—
340C22×C109—81no—
341C22×C109—81no—
342C22×C109—81no—
343C22×C109—81no—
344C22×C109—81no—
345C22×C109—81no—
346C22×C109—81no—
347C22×C109—81no—
348C22×C109—81no—
349C22×C109—81no—
350C22×C109#53411yescharacteristic
351C22×C109#53511yescharacteristic
352C22×C109#53711yescharacteristic
353C22×C109#57611yescharacteristic
354C22×C109#57611yescharacteristic
355C22×C109#57611yescharacteristic
356C22×C109#57711yescharacteristic
357C4×C109—41no—
358C4×C109—41no—
359C4×C109—41no—
360C4×C109—41no—
361C4×C109—41no—
362C4×C109—81no—
363C4×C109—81no—
364C4×C109—81no—
365C4×C109—81no—
366C4×C109—81no—
367C4×C109#56011yescharacteristic
368C4×C109#56011yescharacteristic
369C4×C109#56211yescharacteristic
370C4×C109#56211yescharacteristic
371#32730C10911yesmaximal, characteristic, direct product factor, Sylow
372C2×C109—81no—
373C2×C109—161no—
374C2×C109—161no—
375C2×C109—161no—
376C2×C109#281311yescharacteristic
377C2×C109#319811yescharacteristic
378C2×C109#319911yescharacteristic
379C2×C109#322011yescharacteristic
380C2×C109#322411yescharacteristic
381C2×C109#325711yescharacteristic
382C2×C109#325911yescharacteristic
383#2624C2×C10911yescharacteristic, complemented
384#2619C2×C10911yescharacteristic, complemented
385#2101C2×C10911yescharacteristic, complemented
386#2092C2×C10911yescharacteristic, complemented
387#2067C2×C10911yescharacteristic, complemented
388#2065C2×C10911yescharacteristic, complemented
389#2054C2×C10911yescharacteristic, complemented
390#2054C2×C10911yescharacteristic, complemented
391#2041C2×C10911yescharacteristic, complemented
392#2034C2×C10911yescharacteristic, complemented
393#2033C2×C10911yescharacteristic, complemented
394#2011C2×C10911yescharacteristic, complemented
395#1999C2×C10911yescharacteristic, complemented
396#1999C2×C10911yescharacteristic, complemented
397#1798C2×C10911yescharacteristic, complemented
398C109#3273011yescharacteristic, direct product factor, Sylow
399C22×D8C22×C10911yescharacteristic
400C22×D8C22×C10911yescharacteristic
401C2×#127C22×C10911yescharacteristic
402C2×#121C22×C10911yescharacteristic
403C2×#121C22×C10911yescharacteristic
404C2×#121C22×C10911yescharacteristic
405C2×#117C22×C10911yescharacteristic
406C2×#107C22×C10911yescharacteristic
407C2×#106C22×C10911yescharacteristic
408C2×C4⋊C8C22×C10911yescharacteristic
409C2×C4⋊C8C22×C10911yescharacteristic
410C2×#102C22×C10911yescharacteristic
411C2×#102C22×C10911yescharacteristic
412C2×#102C22×C10911yescharacteristic
413C2×#102C22×C10911yescharacteristic
414C2×#102C22×C10911yescharacteristic
415C2×#102C22×C10911yescharacteristic
416C2×#102C22×C10911yescharacteristic
417C2×#102C22×C10911yescharacteristic
418C2×C22⋊C8C22×C10911yescharacteristic
419C2×C22⋊C8C22×C10911yescharacteristic
420#399—21no—
421#397—21no—
422#394—21no—
423#394—21no—
424#394—21no—
425#394—21no—
426#392—21no—
427#392—21no—
428#390C22×C10911yescharacteristic
429#390C22×C10911yescharacteristic
430#390C22×C10911yescharacteristic
431#390C22×C10911yescharacteristic
432#389C22×C10911yescharacteristic
433#389C22×C10911yescharacteristic
434#382C22×C10911yescharacteristic
435#380C22×C10911yescharacteristic
436#340C22×C10911yescharacteristic
437#340C22×C10911yescharacteristic
438#340C22×C10911yescharacteristic
439#340C22×C10911yescharacteristic
440#336C22×C10911yescharacteristic
441#336C22×C10911yescharacteristic
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C23×C10911yescharacteristic
448C22×D4C23×C10911yescharacteristic
449C22×D4C23×C10911yescharacteristic
450C23×C4C23×C10911yescharacteristic
451C2×D8—41no—
452C2×D8—41no—
453C2×D8—41no—
454C2×D8—41no—
455C2×D8—41no—
456C2×D8—41no—
457C22×C8C23×C10911yescharacteristic
458C22×C8C23×C10911yescharacteristic
459C22×C8C23×C10911yescharacteristic
460C22×C8C23×C10911yescharacteristic
461#127—41no—
462#127—41no—
463#121—41no—
464#121—41no—
465#121—41no—
466#121—41no—
467#121—41no—
468#121—41no—
469#117—41no—
470#117—41no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4D4×C10911yescharacteristic
474C2×C4⋊C4D4×C10911yescharacteristic
475C2×C4⋊C4C23×C10911yescharacteristic
476C2×C4⋊C4C23×C10911yescharacteristic
477C2×C4⋊C4C23×C10911yescharacteristic
478C2×C4⋊C4C23×C10911yescharacteristic
479C2×C4⋊C4C23×C10911yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4D4×C10911yescharacteristic
493C2×C22⋊C4D4×C10911yescharacteristic
494C2×C42C23×C10911yescharacteristic
495C2×C42C23×C10911yescharacteristic
496#107—41no—
497#106—41no—
498C4⋊C8—41no—
499C4⋊C8—41no—
500#102—41no—
501#102—41no—
502#102—41no—
503#102—41no—
504#102—41no—
505#102—41no—
506#102—41no—
507#102—41no—
508C22⋊C8—41no—
509C22⋊C8—41no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24C2×D4×C10911yescharacteristic
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—81no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—81no—
549C2×D4—81no—
550C2×D4—81no—
551C2×D4—81no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4C2×D4×C10911yescharacteristic
564C22×C4C2×D4×C10911yescharacteristic
565C22×C4C2×D4×C10911yescharacteristic
566C22×C4C2×D4×C10911yescharacteristic
567C22×C4C2×D4×C10911yescharacteristic
568C22×C4C24×C10911yescharacteristic
569D8—44no—
570D8—44no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—81no—
596C4⋊C4—81no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23C22×D4×C10911yescharacteristic
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658D4—84no—
659D4—84no—
660D4—84no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4H(5,𝔽2)×C10911yescharacteristic
696C2×C4H(5,𝔽2)×C10911yescharacteristic
697C2×C4H(5,𝔽2)×C10911yescharacteristic
698C2×C4H(5,𝔽2)×C10911yescharacteristic
699C2×C4H(5,𝔽2)×C10911yescharacteristic
700C2×C42−1+4×C10911yescharacteristic
701C8—41no—
702C8—41no—
703C8—41no—
704C8—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22#534×C10911yescharacteristic
734C22#535×C10911yescharacteristic
735C22#537×C10911yescharacteristic
736C22#576×C10911yescharacteristic
737C22#576×C10911yescharacteristic
738C22#576×C10911yescharacteristic
739C22#577×C10911yescharacteristic
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4—81no—
750C4#560×C10911yescharacteristic
751C4#560×C10911yescharacteristic
752C4#562×C10911yescharacteristic
753C4#562×C10911yescharacteristic
754C2—81no—
755C2—161no—
756C2—161no—
757C2—161no—
758C2C109×#281311yescharacteristic
759C2C109×#319811yescharacteristic
760C2C109×#319911yescharacteristic
761C2C109×#322011yescharacteristic
762C2C109×#322411yescharacteristic
763C2C109×#325711yescharacteristic
764C2C109×#325911yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×#117×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#2624C2semidirect
2. C109×#2619C2semidirect
3. C109×#2101C2semidirect
4. C109×#2092C2semidirect
5. C109×#2067C2semidirect
6. C109×#2065C2semidirect
7. C109×#2054C2semidirect
8. C109×#2054C2semidirect
9. C109×#2041C2semidirect
10. C109×#2034C2semidirect
11. C109×#2033C2semidirect
12. C109×#2011C2semidirect
13. C109×#1999C2semidirect
14. C109×#1999C2semidirect
15. C109×#1798C2semidirect
371. #32730C109direct (N × H)
383. #2624C2×C109semidirect
384. #2619C2×C109semidirect
385. #2101C2×C109semidirect
386. #2092C2×C109semidirect
387. #2067C2×C109semidirect
388. #2065C2×C109semidirect
389. #2054C2×C109semidirect
390. #2054C2×C109semidirect
391. #2041C2×C109semidirect
392. #2034C2×C109semidirect
393. #2033C2×C109semidirect
394. #2011C2×C109semidirect
395. #1999C2×C109semidirect
396. #1999C2×C109semidirect
397. #1798C2×C109semidirect
398. C109#32730direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#26242
C109×#26192
C109×#21012
C109×#20922
C109×#20672
C109×#20652
C109×#20542
C109×#20412
C109×#20342
C109×#20332
C109×#20112
C109×#19992
C109×#17982
#32730109