Finite Group Databasebeta

← C2×#22622210 #33962865

Subgroups — C2×#22622210 #33962865

Order 18688.

2082 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989305C211yesmaximal, characteristic
2C2×Q8×C22⋊D73C211yesmaximal, characteristic
3#22622210C2116yesmaximal, direct product factor
4C2×#17988936C211yesmaximal, characteristic, complemented
5C2×#17988928C211yesmaximal, characteristic, complemented
6C2×#17988926C211yesmaximal, characteristic, complemented
7C2×#17988870C211yesmaximal, characteristic, complemented
8C2×#17988845C211yesmaximal, characteristic, complemented
9C2×#17988844C211yesmaximal, characteristic, complemented
10C2×#17988796C211yesmaximal, characteristic, complemented
11C2×#17988744C211yesmaximal, characteristic, complemented
12C2×#17988743C211yesmaximal, characteristic, complemented
13C2×#17988679C211yesmaximal, characteristic, complemented
14C2×#17988663C211yesmaximal, characteristic
15C2×#17988594C211yesmaximal, characteristic, complemented
16C2×#419×C73C211yesmaximal, characteristic, complemented
17C22×Q8×D73C2211yescharacteristic
18C22×Dic292C2211yescharacteristic
19C22×#11924018C2211yescharacteristic
20C22×#11924018C2211yescharacteristic
21C22×#11924011C2211yescharacteristic
22#17989305—24no—
23#17989305C2218yes—
24Q8×C22⋊D73—24no—
25Q8×C22⋊D73C2218yes—
26C2×#14556590C2211yescharacteristic
27C2×#14556589—21no—
28C2×#14556589C2211yescharacteristic
29C2×#14556585—21no—
30C2×#14556584—21no—
31C2×#14556577—21no—
32C2×#14556571C2211yescharacteristic
33C2×#14556570—21no—
34C2×#14556570C2211yescharacteristic
35C2×#14556570C2211yescharacteristic
36C2×#14556567—21no—
37C2×#14556567C2211yescharacteristic
38C2×Q8×Dic73C2211yescharacteristic
39C2×C4×Dic146—21no—
40C2×#14556556C2211yescharacteristic
41C2×C4×C22⋊D73—21no—
42C2×C4×C22⋊D73C2211yescharacteristic
43C2×#14556549C2211yescharacteristic
44#17988936C2218yescomplemented
45#17988928C2218yescomplemented
46#17988926C2218yescomplemented
47#17988870C2218yescomplemented
48#17988845C2218yescomplemented
49#17988844C2218yescomplemented
50#17988796C2218yescomplemented
51#17988744C2218yescomplemented
52#17988743C2218yescomplemented
53#17988679C2218yescomplemented
54#17988663C2218yes—
55C2×#14556524C2211yescharacteristic
56C2×#14556523C2211yescharacteristic
57C2×#14556522C2211yescharacteristic
58C2×#14556520C2211yescharacteristic
59#17988594C2218yescomplemented
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556515C2211yescharacteristic
63C2×#14556515C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556514C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C23×Q8×C73C2211yescharacteristic
70C22×M16×C73C2211yescharacteristic
71C2×#117×C73C2211yescharacteristic
72#419×C73C2218yescomplemented
73C2×#103×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#103×C73C2211yescharacteristic
77C22×Dic146—21no—
78C22×Dic146—21no—
79C22×Dic146C2311yescharacteristic
80C22×Dic146C2311yescharacteristic
81C2×Q8×D73—22no—
82C2×Q8×D73—24no—
83C2×Q8×D73—42no—
84C2×Q8×D73C2314yes—
85C22×C22⋊D73D411yescharacteristic
86C22×C4×D73—21no—
87C22×C4×D73C2311yescharacteristic
88C2×Dic292—42no—
89C2×Dic292C2314yes—
90C2×#11924018—24no—
91C2×#11924018—42no—
92C2×#11924018C2314yes—
93C2×#11924018C2314yes—
94C2×#11924011—42no—
95C2×#11924011C2314yes—
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2311yescharacteristic
98#14556590—22no—
99#14556590C2314yes—
100#14556589—28no—
101#14556589—22no—
102#14556589C2314yes—
103#14556585—28no—
104#14556584—28no—
105#14556577—28no—
106#14556571—22no—
107#14556571C2314yes—
108#14556570—28no—
109#14556570—22no—
110#14556570—22no—
111#14556570C2314yes—
112#14556570C2314yes—
113#14556567—22no—
114#14556567—28no—
115#14556567C2314yes—
116Q8×Dic73—22no—
117Q8×Dic73C2314yes—
118C4×Dic146—28no—
119#14556556—22no—
120#14556556C2314yes—
121C4×C22⋊D73—28no—
122C4×C22⋊D73D414yes—
123C4×C22⋊D73C2314yes—
124#14556549—22no—
125#14556549C2314yes—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73—21no—
128C2×C4⋊Dic73C2311yescharacteristic
129C2×C4⋊Dic73C2311yescharacteristic
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007—21no—
135C2×#11924007—21no—
136C2×#11924007—21no—
137C2×#11924007D411yescharacteristic
138C2×C22⋊Dic73—21no—
139C2×C22⋊Dic73—21no—
140C2×C22⋊Dic73D411yescharacteristic
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005—21no—
144C2×#11924005D411yescharacteristic
145C2×C4×Dic73—21no—
146C2×C4×Dic73—21no—
147C2×C4×Dic73—21no—
148C2×C4×Dic73C2311yescharacteristic
149#14556524C2314yes—
150#14556523C2314yes—
151#14556522C2314yes—
152#14556520C2314yes—
153#14556516C2314yes—
154#14556516C2314yes—
155#14556515C2314yes—
156#14556515C2314yes—
157#14556514C2314yes—
158#14556514C2314yes—
159C22⋊#10596831C2314yes—
160#14556503C2314yes—
161C8×Dic73C2314yes—
162C22×Q8×C73—21no—
163C22×Q8×C73—22no—
164C22×Q8×C73—24no—
165C22×Q8×C73—42no—
166C22×Q8×C73C2311yescharacteristic
167C22×Q8×C73C2314yes—
168C22×Q8×C73C2311yescharacteristic
169C23×C4×C73—21no—
170C23×C4×C73C2311yescharacteristic
171C2×M16×C73—42no—
172C2×M16×C73C2314yes—
173C22×C8×C73C2311yescharacteristic
174C22×C8×C73C2311yescharacteristic
175#117×C73—22no—
176#117×C73C2314yes—
177C2×C4⋊C4×C73C2311yescharacteristic
178C2×C4⋊C4×C73C2311yescharacteristic
179C2×C22⋊C4×C73—21no—
180C2×C42×C73—21no—
181#103×C73C2314yes—
182#103×C73C2314yes—
183#103×C73C2314yes—
184#103×C73C2314yes—
185C23×D73C2×D411yescharacteristic
186C2×Dic146—22no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—22no—
190C2×Dic146—21no—
191C2×Dic146—21no—
192C2×Dic146—24no—
193C2×Dic146—24no—
194C2×Dic146—44no—
195C2×Dic146—44no—
196C2×Dic146C2412yes—
197C2×Dic146C2412yes—
198Q8×D73—28no—
199Q8×D73—44no—
200Q8×D73—48no—
201C2×C22⋊D73—24no—
202C2×C22⋊D73C2×D414yes—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73C2×D411yescharacteristic
208C22×Dic73C2×D411yescharacteristic
209C22×Dic73C2×D411yescharacteristic
210C2×C4×D73—22no—
211C2×C4×D73—22no—
212C2×C4×D73—24no—
213C2×C4×D73—44no—
214C2×C4×D73C2×D412yes—
215C2×C4×D73C2412yes—
216Dic292—44no—
217#11924018—28no—
218#11924018—44no—
219#11924011—44no—
220C2×#10596831—22no—
221C2×#10596831—22no—
222C2×#10596831C2412yes—
223C2×#10596831C2412yes—
224C4⋊Dic73—21no—
225C4⋊Dic73—21no—
226C4⋊Dic73—24no—
227C4⋊Dic73—24no—
228C4⋊Dic73C2412yes—
229C4⋊Dic73C2412yes—
230#11924007—24no—
231#11924007—24no—
232#11924007—24no—
233#11924007—24no—
234#11924007—24no—
235#11924007—24no—
236#11924007—24no—
237#11924007C2×D414yes—
238C22⋊Dic73—24no—
239C22⋊Dic73—24no—
240C22⋊Dic73C2×D414yes—
241#11924005—24no—
242#11924005—24no—
243#11924005—24no—
244#11924005C2×D414yes—
245C4×Dic73—24no—
246C4×Dic73—24no—
247C4×Dic73—24no—
248C4×Dic73C2×D412yes—
249C4×Dic73C2412yes—
250C24×C73C2×D411yescharacteristic
251C2×Q8×C73—21no—
252C2×Q8×C73—24no—
253C2×Q8×C73—21no—
254C2×Q8×C73—22no—
255C2×Q8×C73—28no—
256C2×Q8×C73—22no—
257C2×Q8×C73—22no—
258C2×Q8×C73—44no—
259C2×Q8×C73—44no—
260C2×Q8×C73—48no—
261C2×Q8×C73#4114yes—
262C2×Q8×C73C2412yes—
263C2×Q8×C73C2412yes—
264C22×C4×C73—21no—
265C22×C4×C73—22no—
266C22×C4×C73—22no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—24no—
271C22×C4×C73—44no—
272C22×C4×C73C2×D411yescharacteristic
273C22×C4×C73C2×D412yes—
274C22×C4×C73C2412yes—
275C22×C4×C73C2411yescharacteristic
276M16×C73—44no—
277C2×C8×C73—22no—
278C2×C8×C73—22no—
279C2×C8×C73C2412yes—
280C2×C8×C73C2412yes—
281C4⋊C4×C73—21no—
282C4⋊C4×C73—21no—
283C4⋊C4×C73C2412yes—
284C4⋊C4×C73C2412yes—
285C22⋊C4×C73—24no—
286C42×C73—24no—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—22no—
290C23×C73C22×D412yes—
291C23×C73C22×D411yescharacteristic
292C22×D73—22no—
293C22×D73—22no—
294C22×D73—22no—
295C22×D73C22×D412yes—
296Q8×C73—24no—
297Q8×C73—22no—
298Q8×C73—22no—
299Q8×C73—22no—
300Q8×C73—48no—
301Q8×C73—42no—
302Q8×C73C2×#4114yes—
303C2×C4×C73—22no—
304C2×C4×C73—24no—
305C2×C4×C73—22no—
306C2×C4×C73—24no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—48no—
313C2×C4×C73—42no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73C22×D412yes—
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C2×#4112yes—
319C2×C4×C73H(5,𝔽2)12yes—
320C2×C4×C73C2511yescharacteristic
321C22⋊D73—28no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—42no—
329C2×Dic73—42no—
330C2×Dic73—42no—
331C2×Dic73—42no—
332C2×Dic73#13714yes—
333C2×Dic73C22×D412yes—
334C2×Dic73C22×D412yes—
335C2×Dic73C22×D412yes—
336C4×D73—24no—
337C4×D73—22no—
338C4×D73—22no—
339C4×D73—48no—
340Dic146—22no—
341Dic146—22no—
342Dic146—22no—
343Dic146—22no—
344Dic146—48no—
345Dic146—42no—
346Dic146—42no—
347Dic146—48no—
348C8×C73—22no—
349C8×C73—22no—
350#10596831—22no—
351#10596831—22no—
352C22×C73—22no—
353C22×C73—22no—
354C22×C73—22no—
355C22×C73—44no—
356C22×C73#54612yes—
357C22×C73C2×#13712yes—
358C22×C73#57812yes—
359C22×C73C23×D411yescharacteristic
360C2×D73—22no—
361C2×D73—22no—
362C2×D73—22no—
363C2×D73—44no—
364C4×C73—24no—
365C4×C73—22no—
366C4×C73—42no—
367C4×C73—42no—
368C4×C73—42no—
369C4×C73#54612yes—
370C4×C73C22×#4111yescharacteristic
371C4×C73C2×H(5,𝔽2)11yescharacteristic
372Dic73—22no—
373Dic73—22no—
374Dic73—42no—
375Dic73—42no—
376Dic73—42no—
377Dic73—42no—
378Dic73C2×#13714yes—
379C2×#3328—731nomaximal, Sylow
380C2×C73—42no—
381C2×C73#332814yescomplemented
382C2×C73C2×#54611yescharacteristic
383C2×C73C22×#13711yescharacteristic
384C2×C73C2×#57811yescharacteristic
385D73—42no—
386C2×#556—731no—
387C2×D4×Q8—731no—
388#3328—7316no—
389C2×#487—731no—
390C2×#485—731no—
391C2×#485—731no—
392C2×#475—731no—
393C2×#470—731no—
394C2×#470—731no—
395C2×#462—731no—
396C2×#451—731no—
397C2×#451—731no—
398C2×C4×Q16—731no—
399C2×#436—731no—
400C2×#419—731no—
401C2×#419D7311yescharacteristic, complemented
402C73C2×#332811yescharacteristic, complemented, Sylow
403C23×Q8—731no—
404C23×Q8C2×D7311yescharacteristic
405C22×Q16—731no—
406C22×Q16—731no—
407C22×Q16—731no—
408C22×M16—731no—
409C22×M16C2×D7311yescharacteristic
410#556—738no—
411#556—1464no—
412D4×Q8—738no—
413D4×Q8—1464no—
414C2×C4⋊Q8—731no—
415C2×C4⋊Q8—731no—
416C2×C4⋊Q8—1461no—
417C2×#126—1461no—
418C2×#126—1461no—
419C2×#124—1461no—
420C2×C22⋊Q8—731no—
421C2×C22⋊Q8—731no—
422C2×C22⋊Q8—731no—
423C2×C22⋊Q8—731no—
424C2×C22⋊Q8—1461no—
425C2×C22⋊Q8—1461no—
426C2×C4×Q8—731no—
427C2×C4×Q8—731no—
428C2×C4×Q8—1461no—
429C2×C4×D4—731no—
430C2×C4×D4—1461no—
431C2×#117—731no—
432C2×#117C2×D7311yescharacteristic
433#487—738no—
434#485—738no—
435#485—738no—
436#475—738no—
437#470—738no—
438#470—738no—
439#462—738no—
440#451—738no—
441#451—738no—
442C4×Q16—738no—
443#436—738no—
444C2×#107—731no—
445C2×#106—731no—
446C2×#106—731no—
447C2×C4⋊C8—731no—
448#419—738no—
449#419C2×D7318yescomplemented
450C2×#103—731no—
451C2×#103—731no—
452C2×#103—731no—
453C2×#103—731no—
454C2×#103—731no—
455C2×#103—731no—
456C2×#103C2×D7311yescharacteristic
457C2×#103C2×D7311yescharacteristic
458C2×#103C2×D7311yescharacteristic
459C2×#103C2×D7311yescharacteristic
460C2×C22⋊C8—731no—
461C2×C22⋊C8—731no—
462C2×C4×C8—731no—
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—2922no—
468C22×Q8—734no—
469C22×Q8—731no—
470C22×Q8—731no—
471C22×Q8—1461no—
472C22×Q8—1461no—
473C22×Q8—1464no—
474C22×Q8—1462no—
475C22×Q8C22×D7311yescharacteristic
476C22×Q8C22×D7314yes—
477C22×Q8C22×D7311yescharacteristic
478C22×D4—731no—
479C23×C4—21no—
480C23×C4—731no—
481C23×C4—1461no—
482C23×C4C22×D7311yescharacteristic
483C2×Q16—2922no—
484C2×Q16—2922no—
485C2×Q16—734no—
486C2×Q16—734no—
487C2×Q16—734no—
488C2×Q16—1464no—
489C2×M16—42no—
490C2×M16—2922no—
491C2×M16—734no—
492C2×M16C22×D7314yes—
493C22×C8—731no—
494C22×C8—731no—
495C22×C8C22×D7311yescharacteristic
496C22×C8C22×D7311yescharacteristic
497C4⋊Q8—734no—
498C4⋊Q8—734no—
499C4⋊Q8—1462no—
500C4⋊Q8—1462no—
501C4⋊Q8—1468no—
502#126—1468no—
503#126—1468no—
504#124—1468no—
505C22⋊Q8—734no—
506C22⋊Q8—734no—
507C22⋊Q8—734no—
508C22⋊Q8—734no—
509C22⋊Q8—1468no—
510C22⋊Q8—1468no—
511C22⋊Q8—1462no—
512C22⋊Q8—1462no—
513C22⋊Q8—1462no—
514C22⋊Q8—1462no—
515C4×Q8—734no—
516C4×Q8—734no—
517C4×Q8—1468no—
518C4×Q8—1462no—
519C4×Q8—1462no—
520C4×D4—734no—
521C4×D4—734no—
522C4×D4—1468no—
523#117—22no—
524#117—734no—
525#117—1462no—
526#117C22×D7314yes—
527C2×C4⋊C4—731no—
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C4⋊C4—1461no—
531C2×C4⋊C4—1461no—
532C2×C4⋊C4—1461no—
533C2×C4⋊C4—1461no—
534C2×C4⋊C4—1461no—
535C2×C4⋊C4—1461no—
536C2×C4⋊C4—1461no—
537C2×C4⋊C4—1461no—
538C2×C4⋊C4—1461no—
539C2×C4⋊C4C22×D7311yescharacteristic
540C2×C4⋊C4C22×D7311yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—731no—
543C2×C22⋊C4—731no—
544C2×C22⋊C4—1461no—
545C2×C22⋊C4—1461no—
546C2×C22⋊C4—1461no—
547C2×C22⋊C4—1461no—
548C2×C22⋊C4—1461no—
549C2×C42—21no—
550C2×C42—731no—
551C2×C42—1461no—
552C2×C42—1461no—
553C2×C42—1461no—
554#107—734no—
555#106—734no—
556#106—734no—
557C4⋊C8—734no—
558#103—734no—
559#103—734no—
560#103—734no—
561#103—734no—
562#103—734no—
563#103—734no—
564#103C22×D7314yes—
565#103C22×D7314yes—
566#103C22×D7314yes—
567#103C22×D7314yes—
568C22⋊C8—734no—
569C22⋊C8—734no—
570C4×C8—734no—
571C24—731no—
572C24D4×D7311yescharacteristic
573C2×Q8—21no—
574C2×Q8—24no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—28no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—48no—
583C2×Q8—2924no—
584C2×Q8—2924no—
585C2×Q8—2928no—
586C2×Q8—2924no—
587C2×Q8—732no—
588C2×Q8—732no—
589C2×Q8—1464no—
590C2×Q8—1464no—
591C2×Q8—1468no—
592C2×Q8—1462no—
593C2×Q8—1462no—
594C2×Q8—1462no—
595C2×Q8—1462no—
596C2×Q8—1461no—
597C2×Q8—1461no—
598C2×Q8#1192402814yes—
599C2×Q8C23×D7312yes—
600C2×Q8C23×D7312yes—
601C2×D4—734no—
602C2×D4—1464no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—2924no—
612C22×C4—731no—
613C22×C4—731no—
614C22×C4—731no—
615C22×C4—732no—
616C22×C4—732no—
617C22×C4—1464no—
618C22×C4—1461no—
619C22×C4—1461no—
620C22×C4—1461no—
621C22×C4—1461no—
622C22×C4—1462no—
623C22×C4—1462no—
624C22×C4D4×D7312yes—
625C22×C4D4×D7311yescharacteristic
626C22×C4C23×D7312yes—
627C22×C4C23×D7311yescharacteristic
628Q16—2924no—
629Q16—2924no—
630Q16—1468no—
631M16—44no—
632M16—2924no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—732no—
636C2×C8—732no—
637C2×C8—1462no—
638C2×C8—1462no—
639C2×C8C23×D7312yes—
640C2×C8C23×D7312yes—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—734no—
644C4⋊C4—732no—
645C4⋊C4—732no—
646C4⋊C4—1464no—
647C4⋊C4—1464no—
648C4⋊C4—1464no—
649C4⋊C4—1464no—
650C4⋊C4—1464no—
651C4⋊C4—1464no—
652C4⋊C4—1464no—
653C4⋊C4—1464no—
654C4⋊C4—1464no—
655C4⋊C4—1461no—
656C4⋊C4—1461no—
657C4⋊C4C23×D7312yes—
658C4⋊C4C23×D7312yes—
659C22⋊C4—24no—
660C22⋊C4—734no—
661C22⋊C4—734no—
662C22⋊C4—1464no—
663C22⋊C4—1464no—
664C22⋊C4—1464no—
665C22⋊C4—1464no—
666C22⋊C4—1464no—
667C42—24no—
668C42—732no—
669C42—732no—
670C42—1464no—
671C42—1464no—
672C42—1464no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—732no—
677C23—1462no—
678C23—1462no—
679C23—1462no—
680C23C2×D4×D7312yes—
681C23C2×D4×D7311yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—42no—
688Q8—2928no—
689Q8—2928no—
690Q8—2922no—
691Q8—2922no—
692Q8—1462no—
693Q8—1462no—
694Q8—1462no—
695Q8—1462no—
696Q8C2×#1192402814yes—
697D4—1468no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—2928no—
712C2×C4—2922no—
713C2×C4—2922no—
714C2×C4—2922no—
715C2×C4—2922no—
716C2×C4—734no—
717C2×C4—732no—
718C2×C4—732no—
719C2×C4—732no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4—1462no—
725C2×C4—1462no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4—1464no—
729C2×C4C2×D4×D7312yes—
730C2×C4C2×D4×D7311yescharacteristic
731C2×C4C2×#1192402812yes—
732C2×C4#1455663612yes—
733C2×C4C24×D7311yescharacteristic
734C8—22no—
735C8—22no—
736C8—1462no—
737C8—1462no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—2924no—
743C22—1462no—
744C22—1462no—
745C22—1462no—
746C22#1798922712yes—
747C22#137×D7312yes—
748C22#1798940312yes—
749C22C22×D4×D7311yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—2922no—
756C4—2922no—
757C4—2922no—
758C4—2922no—
759C4—734no—
760C4—1462no—
761C4—1462no—
762C4#1798922712yes—
763C4C22×#1192402811yescharacteristic
764C4C2×#1455663611yescharacteristic
765C2—42no—
766C2—2922no—
767C2#2262221014yesdirect product factor
768C2C2×#1798922711yescharacteristic
769C2C2×#137×D7311yescharacteristic
770C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#419×C73C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
hypercenterC2×#419D73
hypocenterC73C2×#3328
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. #22622210C2direct (N × H)
4. C2×#17988936C2semidirect
5. C2×#17988928C2semidirect
6. C2×#17988926C2semidirect
7. C2×#17988870C2semidirect
8. C2×#17988845C2semidirect
9. C2×#17988844C2semidirect
10. C2×#17988796C2semidirect
11. C2×#17988744C2semidirect
12. C2×#17988743C2semidirect
13. C2×#17988679C2semidirect
15. C2×#17988594C2semidirect
16. C2×#419×C73C2semidirect
44. #17988936C22semidirect
45. #17988928C22semidirect
46. #17988926C22semidirect
47. #17988870C22semidirect
48. #17988845C22semidirect
49. #17988844C22semidirect
50. #17988796C22semidirect
51. #17988744C22semidirect
52. #17988743C22semidirect
53. #17988679C22semidirect
59. #17988594C22semidirect
72. #419×C73C22semidirect
381. C2×C73#3328semidirect
401. C2×#419D73semidirect
402. C73C2×#3328semidirect
449. #419C2×D73semidirect
767. C2#22622210direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179893052
C2×Q8×C22⋊D732
#226222102
C2×#179889362
C2×#179889282
C2×#179889262
C2×#179888702
C2×#179888452
C2×#179888442
C2×#179887962
C2×#179887442
C2×#179887432
C2×#179886792
C2×#179886632
C2×#179885942
C2×#419×C732
C2×#332873