Finite Group Databasebeta

← #13559867

Subgroups — #13559867

Order 1792.

2782 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90269C211yesmaximal, characteristic, complemented
2C2×#90239C211yesmaximal, characteristic
3C4×C7×#124C211yesmaximal, characteristic, complemented
4#11740453C211yesmaximal, characteristic, complemented
5#11740438C211yesmaximal, characteristic, complemented
6C4×#6510C211yesmaximal, characteristic, complemented
7C4×#6499C211yesmaximal, characteristic, complemented
8#11734107C211yesmaximal, characteristic, complemented
9#11734052C211yesmaximal, characteristic, complemented
10#11733919C211yesmaximal, characteristic, complemented
11#11733869C211yesmaximal, characteristic, complemented
12#11733402C214yesmaximal, complemented
13#11733266C214yesmaximal, complemented
14#11731701C211yesmaximal, characteristic, complemented
15#11731666C211yesmaximal, characteristic, complemented
16#11731008C214yesmaximal, complemented
17C4×#6448C214yesmaximal, complemented
18C43×D7C211yesmaximal, characteristic, complemented
19C4×#6438C211yesmaximal, characteristic, complemented
20C22×#1157C2212yes—
21C2×C7×#124C2211yescharacteristic
22C2×C4×C7×Q8C2211yescharacteristic
23C2×C4×C7×D4C2211yescharacteristic
24C2×#6510C2211yescharacteristic
25C2×#6509C2211yescharacteristic
26C2×#6507C2211yescharacteristic
27C2×#6503C2211yescharacteristic
28C2×#6501C2211yescharacteristic
29C2×#6499C2211yescharacteristic
30C2×C4×C22⋊D7C2212yes—
31#90269—28no—
32#90239—28no—
33C2×#6460C2211yescharacteristic
34C2×#6459C2212yes—
35C2×#6458C2211yescharacteristic
36C2×#6452C2212yes—
37C2×#6451C2211yescharacteristic
38C2×#6451C2211yescharacteristic
39C2×#6448C2212yes—
40C2×#6448C2214yes—
41C2×#6447C2212yes—
42C2×#6438C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
44C2×#6435C2212yes—
45C2×C42×D7C2211yescharacteristic
46C2×C42×D7C2212yes—
47C2×C42×D7C2211yescharacteristic
48C2×C42×D7C2212yes—
49C2×C42×D7C2211yescharacteristic
50C2×C4×Dic14C2211yescharacteristic
51C2×C4×Dic14C2212yes—
52C7×#391C2211yescharacteristic
53C7×#390C2211yescharacteristic
54C7×#388C2214yes—
55C7×#382C2211yescharacteristic
56C4×C7×C22⋊C4C2214yes—
57C43×C7C2211yescharacteristic
58#90002C2211yescharacteristic
59#89993C2211yescharacteristic
60C4×C22⋊Dic7C2214yes—
61#89762C2214yes—
62#89760C2211yescharacteristic
63#89749C2211yescharacteristic
64#89749C2211yescharacteristic
65#89746C2211yescharacteristic
66#89729C2214yes—
67#89729C2214yes—
68#89729C2214yes—
69#89728C2214yes—
70#89728C2214yes—
71#89723C2214yes—
72#89717C2214yes—
73#89716C2214yes—
74#89712C2214yes—
75#89711C2211yescharacteristic
76C4×(C2×D7)⋊C4C2214yes—
77C4×(C2×D7)⋊C4C2214yes—
78#89708C2211yescharacteristic
79C42×Dic7C2212yes—
80C42×Dic7C2211yescharacteristic
81C42×Dic7C2211yescharacteristic
82C42×Dic7C2211yescharacteristic
83C42×Dic7C2212yes—
84#89701C2211yescharacteristic
85#89442C2214yes—
86#89441C2214yes—
87#89437C2214yes—
88#89437C2214yes—
89#89422C2214yes—
90#89418C2214yes—
91#89418C2214yes—
92#89418C2214yes—
93#36639—71nomaximal, Sylow
94C22×C7×Q8C2311yescharacteristic
95C22×C7×D4C2311yescharacteristic
96C23×C4×C7C2312yes—
97C22×C22⋊D7C2312yes—
98C22×C22⋊D7C2312yes—
99C22×C22⋊D7C2312yes—
100C2×#1157—28no—
101C2×#1157—216no—
102C22×D28C2311yescharacteristic
103C22×D28C2312yes—
104C22×C4×D7C2312yes—
105C22×C4×D7C2312yes—
106C22×C4×D7C2312yes—
107C22×C4×D7C2311yescharacteristic
108C22×C4×D7C2311yescharacteristic
109C22×C4×D7C2311yescharacteristic
110C22×Dic14C2311yescharacteristic
111C22×Dic14C2312yes—
112C22×Dic14C2312yes—
113C7×#124—24no—
114C4×C7×Q8—24no—
115C4×C7×D4—24no—
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C4⋊C4C2311yescharacteristic
118C2×C7×C4⋊C4C2312yes—
119C2×C7×C22⋊C4C2312yes—
120C2×C7×C22⋊C4C2314yes—
121C2×C7×C22⋊C4C2314yes—
122C2×C42×C7C2312yes—
123C2×C42×C7C2311yescharacteristic
124C2×C42×C7C2312yes—
125C2×C42×C7C2312yes—
126C2×C42×C7C2311yescharacteristic
127C2×C42×C7C2311yescharacteristic
128C2×C22⋊Dic7C2312yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131#6510—24no—
132#6509—24no—
133#6507—24no—
134#6503—24no—
135#6501—24no—
136#6499—24no—
137C4×C22⋊D7—28no—
138C2×(C2×D7)⋊C4C2312yes—
139C2×(C2×D7)⋊C4C2312yes—
140C2×(C2×D7)⋊C4C2312yes—
141C2×(C2×D7)⋊C4C2314yes—
142C2×(C2×D7)⋊C4C2312yes—
143C2×(C2×D7)⋊C4C2314yes—
144C2×(C2×D7)⋊C4C2314yes—
145C2×(C2×D7)⋊C4C2314yes—
146C2×C4⋊Dic7C2311yescharacteristic
147C2×C4⋊Dic7C2312yes—
148C2×C4⋊Dic7C2311yescharacteristic
149C2×Dic7⋊C4C2312yes—
150C2×Dic7⋊C4C2312yes—
151C2×Dic7⋊C4C2312yes—
152C2×Dic7⋊C4C2312yes—
153C2×Dic7⋊C4C2312yes—
154C2×Dic7⋊C4C2312yes—
155C2×C4×Dic7C2312yes—
156C2×C4×Dic7C2312yes—
157C2×C4×Dic7C2312yes—
158C2×C4×Dic7C2312yes—
159C2×C4×Dic7C2312yes—
160C2×C4×Dic7C2312yes—
161C2×C4×Dic7C2312yes—
162C2×C4×Dic7C2312yes—
163C2×C4×Dic7C2311yescharacteristic
164C2×C4×Dic7C2311yescharacteristic
165C2×C4×Dic7C2311yescharacteristic
166C2×C4×Dic7C2311yescharacteristic
167C2×C4×Dic7C2312yes—
168C2×C4×Dic7C2311yescharacteristic
169#6460—24no—
170#6459—28no—
171#6458—24no—
172#6452—28no—
173#6451—24no—
174#6451—24no—
175#6448—28no—
176#6448—216no—
177#6447—28no—
178#6438—24no—
179C4×D28—24no—
180#6435—28no—
181C42×D7—28no—
182C42×D7—24no—
183C42×D7—28no—
184C42×D7—24no—
185C42×D7D418yes—
186C4×Dic14—24no—
187C4×Dic14—28no—
188C7×#95C2314yes—
189C7×#95C2314yes—
190C7⋊#95C2314yes—
191C7⋊#95C2314yes—
192C7⋊#95C2314yes—
193C7⋊#95C2314yes—
194C7⋊#95C2314yes—
195C7⋊#95C2314yes—
196C2×#533—71no—
197C2×#532—71no—
198#2862—71no—
199#2862—71no—
200#2861—74no—
201#2858—71no—
202#2858—71no—
203#2850—71no—
204#2850—71no—
205#2850—74no—
206#2850—71no—
207#2850—71no—
208C4×#124—74no—
209C4×#124—71no—
210C4×#124—71no—
211C4×#124—71no—
212C4×#124D711yescharacteristic, complemented
213#2297—74no—
214C2×C43—71no—
215C24×C7C2412yes—
216C23×D7C2412yes—
217C23×D7C2411yescharacteristic
218C2×C7×Q8—22no—
219C2×C7×Q8—22no—
220C2×C7×Q8—22no—
221C2×C7×D4—22no—
222C2×C7×D4—22no—
223C2×C7×D4—22no—
224C22×C4×C7—24no—
225C22×C4×C7—28no—
226C22×C4×C7C2412yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2411yescharacteristic
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C22×C4×C7C2411yescharacteristic
233C22×C4×C7C2411yescharacteristic
234C2×C22⋊D7—24no—
235C2×C22⋊D7—28no—
236C2×C22⋊D7—24no—
237C2×C22⋊D7—24no—
238C2×C22⋊D7—28no—
239C2×C22⋊D7—28no—
240C22×Dic7C2412yes—
241C22×Dic7C2412yes—
242C22×Dic7C2412yes—
243C22×Dic7C2411yescharacteristic
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2411yescharacteristic
247C22×Dic7C2411yescharacteristic
248#1157—432no—
249C2×D28—24no—
250C2×D28—28no—
251C2×D28—22no—
252C2×D28—22no—
253C2×D28—22no—
254C2×C4×D7—24no—
255C2×C4×D7—24no—
256C2×C4×D7—24no—
257C2×C4×D7—24no—
258C2×C4×D7—22no—
259C2×C4×D7—22no—
260C2×C4×D7—24no—
261C2×C4×D7—24no—
262C2×C4×D7—24no—
263C2×C4×D7—24no—
264C2×C4×D7—28no—
265C2×C4×D7C2×D414yes—
266C2×C4×D7C2×D414yes—
267C2×C4×D7C2×D414yes—
268C2×C4×D7#4118yes—
269C2×Dic14—22no—
270C2×Dic14—22no—
271C2×Dic14—22no—
272C2×Dic14—24no—
273C2×Dic14—24no—
274C2×Dic14—28no—
275C2×Dic14—28no—
276C7×C4⋊C4—22no—
277C7×C4⋊C4—22no—
278C7×C4⋊C4—24no—
279C7×C22⋊C4—24no—
280C7×C22⋊C4—28no—
281C7×C22⋊C4—28no—
282C42×C7—24no—
283C42×C7—24no—
284C42×C7—24no—
285C42×C7—22no—
286C42×C7C2×D414yes—
287C42×C7#4114yescomplemented
288C22⋊Dic7—24no—
289C22⋊Dic7—28no—
290C22⋊Dic7—28no—
291(C2×D7)⋊C4—24no—
292(C2×D7)⋊C4—24no—
293(C2×D7)⋊C4—24no—
294(C2×D7)⋊C4—28no—
295(C2×D7)⋊C4—28no—
296(C2×D7)⋊C4—24no—
297(C2×D7)⋊C4—28no—
298(C2×D7)⋊C4—28no—
299C4⋊Dic7—22no—
300C4⋊Dic7—22no—
301C4⋊Dic7—24no—
302Dic7⋊C4—24no—
303Dic7⋊C4—24no—
304Dic7⋊C4—24no—
305Dic7⋊C4—24no—
306Dic7⋊C4—24no—
307Dic7⋊C4—24no—
308C4×Dic7—24no—
309C4×Dic7—24no—
310C4×Dic7—22no—
311C4×Dic7—24no—
312C4×Dic7—24no—
313C4×Dic7—24no—
314C4×Dic7—24no—
315C4×Dic7—24no—
316C4×Dic7—24no—
317C4×Dic7C2×D414yes—
318C4×Dic7C2×D414yes—
319C4×Dic7C2×D414yes—
320C4×Dic7#4118yescomplemented
321C4×Dic7#4114yescomplemented
322C22×#41—72no—
323#533—148no—
324#532—148no—
325C2×C4⋊Q8—71no—
326C2×C4⋊Q8—71no—
327C2×C4⋊Q8—71no—
328C2×#127—71no—
329C2×#125—72no—
330C2×#124—71no—
331C2×#124—71no—
332C2×#124—74no—
333C2×#124—72no—
334C2×#124—71no—
335C2×#124C2×D711yescharacteristic
336C2×C22⋊Q8—71no—
337C2×C22⋊Q8—72no—
338C2×C22⋊Q8—71no—
339C2×#121—71no—
340C2×#121—71no—
341C2×#121—72no—
342C2×C4×Q8—72no—
343C2×C4×Q8—71no—
344C2×C4×Q8C2×D711yescharacteristic
345C2×C4×D4—72no—
346C2×C4×D4—71no—
347C2×C4×D4C2×D711yescharacteristic
348C2×#117—72no—
349C22×C42—71no—
350C22×C42—71no—
351C22×C42—72no—
352C22×C42—71no—
353C22×C42—72no—
354#391—71no—
355#391—71no—
356#391—71no—
357#391—74no—
358#391—74no—
359#391—74no—
360#391C2×D711yescharacteristic
361#390—71no—
362#390—71no—
363#390—74no—
364#390—74no—
365#390—74no—
366#390—71no—
367#390C2×D711yescharacteristic
368#388—74no—
369#388—74no—
370#388—74no—
371#388—74no—
372#388—74no—
373#388—74no—
374#388—74no—
375#388C2×D714yes—
376#386—74no—
377#386—74no—
378#386—74no—
379#386—74no—
380#382—71no—
381#382—71no—
382#382—71no—
383#382—74no—
384#382C2×D711yescharacteristic
385C4×C22⋊C4—74no—
386C4×C22⋊C4—74no—
387C4×C22⋊C4—74no—
388C4×C22⋊C4C2×D714yes—
389C43—71no—
390C43—71no—
391C43—72no—
392C43—72no—
393C43—71no—
394C43C2×D711yescharacteristic
395C23×C7—22no—
396C23×C7—22no—
397C23×C7—24no—
398C23×C7—22no—
399C23×C7—24no—
400C23×C7C2511yescharacteristic
401C22×D7—21no—
402C22×D7—22no—
403C22×D7—21no—
404C22×D7—22no—
405C22×D7—22no—
406C22×D7—22no—
407C22×D7—24no—
408C22×D7—24no—
409C22×D7C22×D412yes—
410C22×D7C2×#4114yes—
411C7×Q8—44no—
412C7×D4—44no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—24no—
423C2×C4×C7—22no—
424C2×C4×C7—24no—
425C2×C4×C7—48no—
426C2×C4×C7C22×D412yes—
427C2×C4×C7C22×D412yes—
428C2×C4×C7C22×D412yes—
429C2×C4×C7C2×#4114yes—
430C2×C4×C7C2×#4112yes—
431C2×C4×C7C2×#4114yes—
432C2×C4×C7C2×#4114yes—
433C2×C4×C7C2×#4112yes—
434C22⋊D7—48no—
435C22⋊D7—48no—
436C22⋊D7—48no—
437C2×Dic7—21no—
438C2×Dic7—22no—
439C2×Dic7—21no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—24no—
448C2×Dic7—22no—
449C2×Dic7—24no—
450C2×Dic7C22×D412yes—
451C2×Dic7C22×D412yes—
452C2×Dic7C22×D412yes—
453C2×Dic7C2×#4114yes—
454C2×Dic7C2×#4114yes—
455C2×Dic7C2×#4114yes—
456C2×Dic7C2×#4114yes—
457D28—48no—
458D28—44no—
459C4×D7—216no—
460C4×D7—216no—
461C4×D7—28no—
462C4×D7—28no—
463C4×D7—48no—
464C4×D7#124116yescomplemented
465Dic14—44no—
466Dic14—48no—
467Dic14—48no—
468C2×#41—148no—
469C2×#41—1416no—
470C22×Q8—72no—
471C22×Q8—71no—
472C22×Q8—72no—
473C22×Q8C22×D711yescharacteristic
474C22×D4—72no—
475C22×D4—72no—
476C22×D4—72no—
477C22×D4—71no—
478C22×D4—72no—
479C22×D4C22×D711yescharacteristic
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—72no—
484C23×C4—72no—
485C23×C4—72no—
486C23×C4C22×D712yes—
487C4⋊Q8—144no—
488C4⋊Q8—144no—
489C4⋊Q8—144no—
490#127—144no—
491#125—148no—
492#124—24no—
493#124—148no—
494#124—1416no—
495#124—144no—
496#124—144no—
497#124—144no—
498C22⋊Q8—148no—
499C22⋊Q8—144no—
500C22⋊Q8—144no—
501#121—148no—
502#121—144no—
503#121—144no—
504C4×Q8—24no—
505C4×Q8—148no—
506C4×Q8—144no—
507C4×D4—24no—
508C4×D4—148no—
509C4×D4—144no—
510#117—148no—
511C2×C4⋊C4—72no—
512C2×C4⋊C4—72no—
513C2×C4⋊C4—72no—
514C2×C4⋊C4—71no—
515C2×C4⋊C4—72no—
516C2×C4⋊C4—72no—
517C2×C4⋊C4—72no—
518C2×C4⋊C4—72no—
519C2×C4⋊C4—71no—
520C2×C4⋊C4C22×D711yescharacteristic
521C2×C4⋊C4C22×D712yes—
522C2×C4⋊C4C22×D711yescharacteristic
523C2×C22⋊C4—72no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—72no—
527C2×C22⋊C4—72no—
528C2×C22⋊C4—72no—
529C2×C22⋊C4—72no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—74no—
532C2×C22⋊C4—74no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4C22×D712yes—
535C2×C22⋊C4C22×D714yes—
536C2×C22⋊C4C22×D714yes—
537C2×C42—71no—
538C2×C42—72no—
539C2×C42—71no—
540C2×C42—71no—
541C2×C42—71no—
542C2×C42—78no—
543C2×C42—72no—
544C2×C42—72no—
545C2×C42—72no—
546C2×C42—72no—
547C2×C42—72no—
548C2×C42—72no—
549C2×C42—71no—
550C2×C42—72no—
551C2×C42—72no—
552C2×C42—148no—
553C2×C42—144no—
554C2×C42—148no—
555C2×C42—144no—
556C2×C42C22×D712yes—
557C2×C42C22×D711yescharacteristic
558C2×C42C22×D712yes—
559C2×C42C22×D712yes—
560C2×C42C22×D711yescharacteristic
561C2×C42C22×D711yescharacteristic
562#95—74no—
563#95—74no—
564#95—74no—
565#95—74no—
566#95—74no—
567#95—74no—
568#95C22×D714yes—
569#95C22×D714yes—
570C22×C7—42no—
571C22×C7—42no—
572C22×C7—42no—
573C22×C7—44no—
574C22×C7—44no—
575C22×C7C23×D411yescharacteristic
576C22×C7C22×#4111yescharacteristic
577C22×C7C22×#4112yes—
578C22×C7C22×#4112yes—
579C22×C7C22×#4111yescharacteristic
580C2×D7—22no—
581C2×D7—22no—
582C2×D7—24no—
583C2×D7—24no—
584C2×D7—42no—
585C2×D7—42no—
586C2×D7—42no—
587C2×D7—44no—
588C2×D7—44no—
589C2×D7C2×#12414yes—
590C4×C7—22no—
591C4×C7—24no—
592C4×C7—24no—
593C4×C7—42no—
594C4×C7—42no—
595C4×C7—42no—
596C4×C7C2×#12414yes—
597C4×C7#53214yes—
598Dic7—22no—
599Dic7—24no—
600Dic7—24no—
601Dic7—42no—
602Dic7—42no—
603Dic7—42no—
604Dic7C2×#12414yes—
605Dic7#53214yes—
606C24—71no—
607C24—72no—
608C24C23×D712yes—
609#41—2832no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—144no—
614C2×Q8—144no—
615C2×Q8—148no—
616C2×Q8—148no—
617C2×Q8—142no—
618C2×Q8—142no—
619C2×Q8—142no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—144no—
624C2×D4—148no—
625C2×D4—144no—
626C2×D4—144no—
627C2×D4—148no—
628C2×D4—148no—
629C2×D4—144no—
630C2×D4—148no—
631C2×D4—142no—
632C2×D4—142no—
633C2×D4—142no—
634C22×C4—24no—
635C22×C4—28no—
636C22×C4—71no—
637C22×C4—71no—
638C22×C4—74no—
639C22×C4—78no—
640C22×C4—72no—
641C22×C4—72no—
642C22×C4—71no—
643C22×C4—74no—
644C22×C4—74no—
645C22×C4—72no—
646C22×C4—72no—
647C22×C4—72no—
648C22×C4—144no—
649C22×C4—144no—
650C22×C4—144no—
651C22×C4—144no—
652C22×C4—144no—
653C22×C4—144no—
654C22×C4—142no—
655C22×C4—144no—
656C22×C4—142no—
657C22×C4—144no—
658C22×C4—148no—
659C22×C4C23×D712yes—
660C22×C4C23×D712yes—
661C22×C4C23×D712yes—
662C22×C4C23×D712yes—
663C22×C4C23×D711yescharacteristic
664C22×C4C23×D712yes—
665C22×C4C23×D711yescharacteristic
666C22×C4C23×D711yescharacteristic
667C4⋊C4—22no—
668C4⋊C4—24no—
669C4⋊C4—22no—
670C4⋊C4—144no—
671C4⋊C4—144no—
672C4⋊C4—144no—
673C4⋊C4—144no—
674C4⋊C4—144no—
675C4⋊C4—144no—
676C4⋊C4—144no—
677C4⋊C4—142no—
678C4⋊C4—142no—
679C22⋊C4—28no—
680C22⋊C4—24no—
681C22⋊C4—28no—
682C22⋊C4—144no—
683C22⋊C4—148no—
684C22⋊C4—148no—
685C22⋊C4—144no—
686C22⋊C4—144no—
687C22⋊C4—144no—
688C22⋊C4—148no—
689C22⋊C4—148no—
690C22⋊C4—148no—
691C22⋊C4—144no—
692C22⋊C4—148no—
693C42—24no—
694C42—24no—
695C42—22no—
696C42—24no—
697C42—74no—
698C42—74no—
699C42—74no—
700C42—78no—
701C42—74no—
702C42—144no—
703C42—144no—
704C42—144no—
705C42—144no—
706C42—144no—
707C42—144no—
708C42—142no—
709C42—144no—
710C42—144no—
711C42#115714yescomplemented
712C42D4×D714yes—
713C2×C7—82no—
714C2×C7C22×#12411yescharacteristic
715C2×C7C2×#53211yescharacteristic
716C2×C7C2×#53211yescharacteristic
717C2×C7#344412yes—
718C2×C7#344412yes—
719D7—24no—
720D7—82no—
721C23—22no—
722C23—22no—
723C23—24no—
724C23—22no—
725C23—24no—
726C23—72no—
727C23—74no—
728C23—141no—
729C23—142no—
730C23—141no—
731C23—142no—
732C23—142no—
733C23—144no—
734C23—142no—
735C23—144no—
736C23C24×D711yescharacteristic
737Q8—44no—
738Q8—288no—
739Q8—288no—
740Q8—284no—
741D4—44no—
742D4—288no—
743D4—288no—
744D4—288no—
745D4—288no—
746D4—284no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—48no—
760C2×C4—72no—
761C2×C4—72no—
762C2×C4—74no—
763C2×C4—74no—
764C2×C4—716no—
765C2×C4—72no—
766C2×C4—74no—
767C2×C4—74no—
768C2×C4—148no—
769C2×C4—1416no—
770C2×C4—1416no—
771C2×C4—141no—
772C2×C4—142no—
773C2×C4—141no—
774C2×C4—142no—
775C2×C4—142no—
776C2×C4—142no—
777C2×C4—148no—
778C2×C4—142no—
779C2×C4—142no—
780C2×C4—142no—
781C2×C4—142no—
782C2×C4—144no—
783C2×C4—142no—
784C2×C4—144no—
785C2×C4—288no—
786C2×C4C2×#115714yes—
787C2×C4C2×#115712yes—
788C2×C4C2×D4×D712yes—
789C2×C4C2×D4×D712yes—
790C2×C4C2×D4×D712yes—
791C2×C4D7×#4114yes—
792C2×C4D7×#4112yes—
793C2×C4D7×#4114yes—
794C7#3663911yescharacteristic, complemented, Sylow
795C22—42no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—44no—
800C22—74no—
801C22—142no—
802C22—142no—
803C22—144no—
804C22—144no—
805C22—282no—
806C22—282no—
807C22—282no—
808C22—284no—
809C22—284no—
810C22C22×#115711yescharacteristic
811C22C22×D4×D711yescharacteristic
812C22C2×D7×#4112yes—
813C22C2×D7×#4111yescharacteristic
814C22C2×D7×#4112yes—
815C4—22no—
816C4—24no—
817C4—24no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—74no—
822C4—74no—
823C4—142no—
824C4—144no—
825C4—144no—
826C4—282no—
827C4—282no—
828C4—282no—
829C4#9023914yes—
830C4D7×#12414yes—
831C2—82no—
832C2—144no—
833C2—562no—
834C2C2×#9023911yescharacteristic
835C2#1174290412yes—
836C2C2×D7×#12411yescharacteristic
837C2#1174318712yes—
838C2D7×#53211yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutator, socle, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC4×C7×#124C2
prime radicalC2×#90239C2
hypercenterC4×#124D7
hypocenterC7#36639
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. C2×#90269C2semidirect
3. C4×C7×#124C2semidirect
4. #11740453C2semidirect
5. #11740438C2semidirect
6. C4×#6510C2semidirect
7. C4×#6499C2semidirect
8. #11734107C2semidirect
9. #11734052C2semidirect
10. #11733919C2semidirect
11. #11733869C2semidirect
12. #11733402C2semidirect
13. #11733266C2semidirect
14. #11731701C2semidirect
15. #11731666C2semidirect
16. #11731008C2semidirect
17. C4×#6448C2semidirect
18. C43×D7C2semidirect
19. C4×#6438C2semidirect
212. C4×#124D7semidirect
287. C42×C7#41semidirect
320. C4×Dic7#41semidirect
321. C4×Dic7#41semidirect
464. C4×D7#124semidirect
711. C42#1157semidirect
794. C7#36639semidirect

Maximal subgroups

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

subgroupindex
C2×#902692
C2×#902392
C4×C7×#1242
#117404532
#117404382
C4×#65102
C4×#64992
#117341072
#117340522
#117339192
#117338692
#117334022
#117332662
#117317012
#117316662
#117310082
C4×#64482
C43×D72
C4×#64382
#366397