Finite Group Databasebeta

← #14223913

Subgroups — #14223913

Order 1792.

1976 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic, complemented
2#11742748C211yesmaximal, characteristic
3#11740793C212yesmaximal, complemented
4#11740792C212yesmaximal, complemented
5#11740791C214yesmaximal, complemented
6#11740790C214yesmaximal, complemented
7#11740789C212yesmaximal, complemented
8#11740788C212yesmaximal, complemented
9#11740652C211yesmaximal, characteristic, complemented
10#11740648C211yesmaximal, characteristic, complemented
11#11740644C211yesmaximal, characteristic, complemented
12#11740643C211yesmaximal, characteristic, complemented
13#11740177C214yesmaximal, complemented
14C4×#6505C214yesmaximal, complemented
15C2×C4×#1136C211yesmaximal, characteristic, complemented
16C7×#533—21no—
17C7×#533—21no—
18C7×#533—21no—
19C7×#533—21no—
20C7×#533C2212yes—
21C7×#533C2212yes—
22C7×#533C2212yes—
23C7×#533C2212yes—
24C2×C7×C4⋊Q8C2211yescharacteristic
25C2×C7×C4⋊Q8C2211yescharacteristic
26C2×C7×#125—21no—
27C2×C7×C22⋊Q8—21no—
28C2×C7×C22⋊Q8C2212yes—
29C2×C4×C7×Q8—21no—
30C2×C4×C7×Q8C2212yes—
31C2×C7×#117—21no—
32C22×C42×C7C2211yescharacteristic
33C2×#6505C2214yes—
34#90482—21no—
35#90482—21no—
36#90482C2212yes—
37C22×#1136C2212yes—
38#90170—21no—
39#90170—21no—
40#90170—21no—
41#90170—21no—
42#90170C2212yes—
43#90170C2212yes—
44#90168C2211yescharacteristic
45#90168C2211yescharacteristic
46#90168C2211yescharacteristic
47C4×#1157—21no—
48C4×#1157—21no—
49C4×#1157C2212yes—
50#90161C2211yescharacteristic
51#90161C2211yescharacteristic
52#90161C2211yescharacteristic
53#89997C2214yes—
54#89865C2212yescomplemented
55#89864C2212yescomplemented
56#89861C2214yescomplemented
57#89860C2212yescomplemented
58#89858C2214yescomplemented
59#89857C2212yescomplemented
60#89854C2214yescomplemented
61#89853C2212yescomplemented
62#89853C2212yescomplemented
63#89852C2214yescomplemented
64#89851C2212yescomplemented
65#89850C2212yescomplemented
66#89824C2218yes—
67#89823C2218yes—
68#89821C2218yes—
69#89820C2218yes—
70#89802C2218yescomplemented
71C4×#1144C2218yescomplemented
72#89798C2218yescomplemented
73C4×#1143C2218yescomplemented
74#89738C2214yes—
75#89736C2214yes—
76C4×#1136C2212yes—
77C4×#1136C2212yes—
78C4×#1136C2212yes—
79C4×#1136C2211yescharacteristic
80C4×#1136C2211yescharacteristic
81C2×#6377C2212yes—
82C2×C4×C7⋊C8C2212yes—
83#60701—71nomaximal, Sylow
84C22×C7×Q8—21no—
85C22×C7×Q8C2312yes—
86C23×C4×C7D411yescharacteristic
87C23×C4×C7D411yescharacteristic
88C23×C4×C7C2311yescharacteristic
89C2×#1157—21no—
90C2×#1157—21no—
91C2×#1157C2312yes—
92C7×C4⋊Q8—21no—
93C7×C4⋊Q8—21no—
94C7×C4⋊Q8—21no—
95C7×C4⋊Q8—21no—
96C7×C4⋊Q8C2312yes—
97C7×C4⋊Q8C2312yes—
98C7×C4⋊Q8C2312yes—
99C7×C4⋊Q8C2312yes—
100C7×#125—22no—
101C7×#125—22no—
102C7×#125—22no—
103C7×#125—22no—
104C7×C22⋊Q8—22no—
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8—22no—
107C7×C22⋊Q8—22no—
108C7×C22⋊Q8—22no—
109C7×C22⋊Q8—22no—
110C7×C22⋊Q8C2314yes—
111C7×C22⋊Q8C2314yes—
112C4×C7×Q8—22no—
113C4×C7×Q8—22no—
114C4×C7×Q8—22no—
115C4×C7×Q8—22no—
116C4×C7×Q8—22no—
117C4×C7×Q8—22no—
118C4×C7×Q8C2314yes—
119C4×C7×Q8C2314yes—
120C7×#117—22no—
121C7×#117—22no—
122C7×#117—22no—
123C7×#117—22no—
124C2×C7×C4⋊C4—21no—
125C2×C7×C4⋊C4—21no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4—22no—
128C2×C7×C4⋊C4—22no—
129C2×C7×C4⋊C4C2312yes—
130C2×C7×C22⋊C4—22no—
131C2×C42×C7—22no—
132C2×C42×C7D411yescharacteristic
133C2×C42×C7D411yescharacteristic
134C2×C42×C7D411yescharacteristic
135C2×C42×C7D411yescharacteristic
136C2×C42×C7D411yescharacteristic
137C2×C42×C7D411yescharacteristic
138C2×C42×C7C2311yescharacteristic
139C2×C42×C7C2311yescharacteristic
140C2×C42×C7C2311yescharacteristic
141C2×C42×C7C2311yescharacteristic
142C2×C42×C7C2311yescharacteristic
143C2×C42×C7C2311yescharacteristic
144#6516—22no—
145C2×#1144C2318yes—
146#6505—216no—
147C2×#1143C2318yes—
148#6493—21no—
149#6493—21no—
150#6493—21no—
151#6493—21no—
152#6493C2312yes—
153#6493C2312yes—
154#6492—22no—
155#6492—22no—
156#6492—22no—
157C4×C22⋊D7—22no—
158C4×C22⋊D7—22no—
159C4×C22⋊D7—22no—
160C4×C22⋊D7—22no—
161C4×C22⋊D7—22no—
162C4×C22⋊D7—22no—
163#6489—21no—
164#6489—21no—
165#6489C2312yes—
166#6487—21no—
167#6487—21no—
168#6487—21no—
169#6487—21no—
170#6487C2312yes—
171#6487C2312yes—
172C2×#1136—28no—
173C2×#1136C2312yes—
174C2×#1136C2314yes—
175C2×#1136C2312yes—
176C22×C7⋊C8C2314yes—
177#6439—22no—
178#6439—22no—
179#6438—21no—
180#6438—21no—
181#6438C2312yes—
182#6437C2311yescharacteristic
183C4×D28—21no—
184C4×D28—21no—
185C4×D28—21no—
186C4×D28—21no—
187C4×D28C2312yes—
188C4×D28C2312yes—
189#6435—22no—
190#6435—22no—
191#6435—22no—
192C42×D7—22no—
193#6433—21no—
194#6433—21no—
195#6433C2312yes—
196#6432C2311yescharacteristic
197#6432C2311yescharacteristic
198#6432C2311yescharacteristic
199C4×Dic14—21no—
200C4×Dic14—21no—
201C4×Dic14—21no—
202C4×Dic14—21no—
203C4×Dic14C2312yes—
204C4×Dic14C2312yes—
205#6409C2318yes—
206#6409C2318yes—
207#6384C2318yes—
208#6383C2318yes—
209#6382C2318yes—
210#6381C2318yes—
211#6377C2312yes—
212#6377C2312yes—
213#6377C2314yes—
214C4×C7⋊C8C2312yes—
215C4×C7⋊C8C2312yes—
216C4×C7⋊C8C2314yes—
217#3444—71no—
218C2×#533D711yescharacteristic, complemented
219#3185—72no—
220#3182—72no—
221#3181—74no—
222#3172—74no—
223#3170—72no—
224#3167—72no—
225#3165—71no—
226#3152—71no—
227#3141—71no—
228#3139—71no—
229#3056—74no—
230C4×#137—74no—
231C2×C4×M16—71no—
232C24×C7C2×D411yescharacteristic
233C2×C7×Q8—22no—
234C2×C7×Q8—22no—
235C2×C7×Q8—22no—
236C2×C7×Q8—28no—
237C2×C7×Q8—44no—
238C2×C7×Q8C2414yes—
239C22×C4×C7—24no—
240C22×C4×C7—24no—
241C22×C4×C7—22no—
242C22×C4×C7—22no—
243C22×C4×C7—42no—
244C22×C4×C7C2×D411yescharacteristic
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D411yescharacteristic
249C22×C4×C7C2×D411yescharacteristic
250C22×C4×C7C2×D411yescharacteristic
251C22×C4×C7C2×D411yescharacteristic
252C22×C4×C7C2×D411yescharacteristic
253C22×C4×C7C2×D411yescharacteristic
254C22×C4×C7C2×D411yescharacteristic
255C22×C4×C7C2×D411yescharacteristic
256C22×C4×C7C2×D411yescharacteristic
257C22×C4×C7C2×D411yescharacteristic
258C22×C4×C7C2×D411yescharacteristic
259C22×C4×C7C2411yescharacteristic
260C22×C4×C7C2411yescharacteristic
261C22×C4×C7C2411yescharacteristic
262C2×C22⋊D7—22no—
263C2×C22⋊D7—22no—
264C2×C22⋊D7—22no—
265#1157—28no—
266#1157—44no—
267#1157—44no—
268C2×D28—21no—
269C2×D28—21no—
270C2×D28C2412yes—
271C2×C4×D7—22no—
272C2×C4×D7—22no—
273C2×C4×D7—22no—
274C2×Dic14—21no—
275C2×Dic14—21no—
276C2×Dic14C2412yes—
277C7×C4⋊C4—22no—
278C7×C4⋊C4—22no—
279C7×C4⋊C4—22no—
280C7×C4⋊C4—22no—
281C7×C4⋊C4—22no—
282C7×C4⋊C4—22no—
283C7×C4⋊C4—24no—
284C7×C4⋊C4—24no—
285C7×C4⋊C4—24no—
286C7×C4⋊C4—24no—
287C7×C4⋊C4—22no—
288C7×C4⋊C4C2414yes—
289C7×C22⋊C4—24no—
290C7×C22⋊C4—24no—
291C42×C7—24no—
292C42×C7—24no—
293C42×C7C2×D411yescharacteristic
294C42×C7C2×D411yescharacteristic
295C42×C7C2×D411yescharacteristic
296C42×C7C2×D411yescharacteristic
297C42×C7C2×D411yescharacteristic
298C42×C7C2×D411yescharacteristic
299C42×C7C2×D411yescharacteristic
300C42×C7C2×D411yescharacteristic
301C42×C7C2×D411yescharacteristic
302C42×C7C2×D411yescharacteristic
303C42×C7C2×D411yescharacteristic
304C42×C7C2×D411yescharacteristic
305C42×C7C2411yescharacteristic
306C42×C7C2411yescharacteristic
307C42×C7C2411yescharacteristic
308C42×C7C2411yescharacteristic
309C22⋊Dic7—22no—
310C22⋊Dic7—22no—
311C22⋊Dic7—22no—
312#1144—216no—
313#1143—216no—
314(C2×D7)⋊C4—22no—
315(C2×D7)⋊C4—22no—
316(C2×D7)⋊C4—22no—
317(C2×D7)⋊C4—22no—
318(C2×D7)⋊C4—22no—
319(C2×D7)⋊C4—22no—
320C4⋊Dic7—21no—
321C4⋊Dic7—21no—
322C4⋊Dic7—21no—
323C4⋊Dic7—21no—
324C4⋊Dic7C2412yes—
325C4⋊Dic7C2412yes—
326Dic7⋊C4—22no—
327Dic7⋊C4—22no—
328Dic7⋊C4—22no—
329Dic7⋊C4—22no—
330Dic7⋊C4—22no—
331Dic7⋊C4—22no—
332C4×Dic7—22no—
333C4×Dic7—22no—
334C4×Dic7—22no—
335#1136—24no—
336#1136—28no—
337#1136#4118yescomplemented
338C2×C7⋊C8—28no—
339C2×C7⋊C8C2414yes—
340C2×C7⋊C8C2414yes—
341C2×#137—74no—
342C22×M16—72no—
343#533—21no—
344#533—21no—
345#533—21no—
346#533—21no—
347#533—71no—
348#533—71no—
349#533—71no—
350#533C2×D712yes—
351#533C2×D712yes—
352#533C2×D712yes—
353#533C2×D712yes—
354#532—71no—
355#532—71no—
356#532—71no—
357C2×C4⋊Q8C2×D711yescharacteristic
358C2×C4⋊Q8C2×D711yescharacteristic
359#529—72no—
360#529—72no—
361#529—141no—
362#529—141no—
363#529—141no—
364#529—141no—
365C2×#125—21no—
366#525—72no—
367#525—141no—
368#525—141no—
369C2×C22⋊Q8—21no—
370C2×C22⋊Q8C2×D712yes—
371C4×#41—72no—
372C4×#41—141no—
373C4×#41—141no—
374C2×C4×Q8—21no—
375C2×C4×Q8C2×D712yes—
376C2×#117—21no—
377C22×C42C2×D711yescharacteristic
378#501—74no—
379#500—72no—
380#498—72no—
381#497—74no—
382#494—72no—
383#492—72no—
384#491—74no—
385#489—74no—
386#487—72no—
387#487—72no—
388#487—72no—
389#486—72no—
390#470—78no—
391#468—78no—
392#467—78no—
393#465—78no—
394#441—78no—
395#440—78no—
396C4×Q16—78no—
397C4×SD16—78no—
398#428—74no—
399#419—74no—
400#417—74no—
401C4×M16—71no—
402C4×M16—71no—
403C4×M16—72no—
404C4×M16—72no—
405C4×M16—72no—
406C2×#97—72no—
407C2×C4×C8—72no—
408C23×C7—22no—
409C23×C7—22no—
410C23×C7—41no—
411C23×C7C22×D411yescharacteristic
412C23×C7C22×D411yescharacteristic
413C23×C7C22×D411yescharacteristic
414C22×D7—22no—
415C7×Q8—28no—
416C7×Q8—44no—
417C7×Q8—44no—
418C7×Q8—44no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—24no—
433C2×C4×C7—24no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—44no—
438C2×C4×C7—44no—
439C2×C4×C7#13714yescomplemented
440C2×C4×C7C22×D411yescharacteristic
441C2×C4×C7C22×D411yescharacteristic
442C2×C4×C7C22×D411yescharacteristic
443C2×C4×C7C22×D411yescharacteristic
444C2×C4×C7C22×D411yescharacteristic
445C2×C4×C7C22×D411yescharacteristic
446C2×C4×C7C22×D411yescharacteristic
447C2×C4×C7C22×D411yescharacteristic
448C2×C4×C7C22×D411yescharacteristic
449C2×C4×C7C22×D411yescharacteristic
450C2×C4×C7C22×D411yescharacteristic
451C2×C4×C7C2×#4114yes—
452C2×C4×C7C2511yescharacteristic
453C22⋊D7—44no—
454C22⋊D7—44no—
455C22⋊D7—44no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459D28—24no—
460D28—42no—
461D28—42no—
462C4×D7—44no—
463C4×D7—44no—
464C4×D7—44no—
465Dic14—24no—
466Dic14—42no—
467Dic14—42no—
468C7⋊C8—24no—
469C7⋊C8C2×#4118yes—
470C2×#41—72no—
471C2×#41—141no—
472C2×#41—141no—
473C22×Q8—21no—
474C22×Q8C22×D712yes—
475C23×C4C22⋊D711yescharacteristic
476C23×C4C22⋊D711yescharacteristic
477C23×C4C22×D711yescharacteristic
478#137—1416no—
479C2×Q16—78no—
480C2×SD16—78no—
481C2×M16—72no—
482C2×M16—72no—
483C2×M16—74no—
484C2×M16—148no—
485C22×C8—74no—
486C4⋊Q8—21no—
487C4⋊Q8—21no—
488C4⋊Q8—21no—
489C4⋊Q8—21no—
490C4⋊Q8—71no—
491C4⋊Q8—71no—
492C4⋊Q8—71no—
493C4⋊Q8C22×D712yes—
494C4⋊Q8C22×D712yes—
495C4⋊Q8C22×D712yes—
496C4⋊Q8C22×D712yes—
497#127—71no—
498#126—142no—
499#126—142no—
500#125—22no—
501#125—22no—
502#125—22no—
503#125—22no—
504#125—72no—
505#125—141no—
506#125—141no—
507#124—72no—
508#124—141no—
509#124—141no—
510#123—142no—
511#123—142no—
512#123—142no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—22no—
518C22⋊Q8—22no—
519C22⋊Q8—72no—
520C22⋊Q8—72no—
521C22⋊Q8—141no—
522C22⋊Q8—141no—
523C22⋊Q8—141no—
524C22⋊Q8—141no—
525C22⋊Q8C22×D714yes—
526C22⋊Q8C22×D714yes—
527#121—72no—
528#121—72no—
529#121—141no—
530#121—141no—
531#121—141no—
532#121—141no—
533#120—142no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—72no—
541C4×Q8—72no—
542C4×Q8—141no—
543C4×Q8—141no—
544C4×Q8—141no—
545C4×Q8—141no—
546C4×Q8C22×D714yes—
547C4×Q8C22×D714yes—
548C4×D4—72no—
549C4×D4—72no—
550C4×D4—142no—
551C4×D4—142no—
552C4×D4—142no—
553C4×D4—142no—
554C4×D4—142no—
555C4×D4—142no—
556C4×D4—141no—
557C4×D4—141no—
558C4×D4—141no—
559C4×D4—141no—
560#117—22no—
561#117—22no—
562#117—22no—
563#117—22no—
564#117—72no—
565#117—141no—
566#117—141no—
567#117—142no—
568#117—142no—
569#117—142no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4C22×D712yes—
576C2×C22⋊C4—22no—
577C2×C42—22no—
578C2×C42—142no—
579C2×C42C22⋊D711yescharacteristic
580C2×C42C22⋊D711yescharacteristic
581C2×C42C22⋊D711yescharacteristic
582C2×C42C22⋊D711yescharacteristic
583C2×C42C22⋊D711yescharacteristic
584C2×C42C22⋊D711yescharacteristic
585C2×C42C22×D711yescharacteristic
586C2×C42C22×D711yescharacteristic
587C2×C42C22×D711yescharacteristic
588C2×C42C22×D711yescharacteristic
589C2×C42C22×D711yescharacteristic
590C2×C42C22×D711yescharacteristic
591#107—78no—
592#106—78no—
593#103—78no—
594#103—78no—
595#103—78no—
596#102—78no—
597#97—74no—
598#97—72no—
599#97—72no—
600C4×C8—74no—
601C4×C8—72no—
602C4×C8—72no—
603C22×C7—21no—
604C22×C7—21no—
605C22×C7—21no—
606C22×C7—21no—
607C22×C7—21no—
608C22×C7—21no—
609C22×C7—21no—
610C22×C7—44no—
611C22×C7#53212yes—
612C22×C7C2×#13712yes—
613C22×C7C23×D411yescharacteristic
614C2×D7—42no—
615C2×D7—42no—
616C2×D7—42no—
617C4×C7—21no—
618C4×C7—21no—
619C4×C7—21no—
620C4×C7—21no—
621C4×C7—21no—
622C4×C7—21no—
623C4×C7—21no—
624C4×C7—44no—
625C4×C7—44no—
626C4×C7#53212yes—
627C4×C7C2×#13712yes—
628C4×C7C2×#13712yes—
629C4×C7#57512yes—
630C4×C7C22×#4112yes—
631Dic7—42no—
632Dic7—42no—
633Dic7—42no—
634C24C2×C22⋊D711yescharacteristic
635#41—148no—
636#41—284no—
637#41—284no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—28no—
642C2×Q8—44no—
643C2×Q8—72no—
644C2×Q8—141no—
645C2×Q8—141no—
646C2×Q8C23×D714yes—
647C2×D4—72no—
648C2×D4—142no—
649C2×D4—142no—
650C2×D4—142no—
651C2×D4—141no—
652C2×D4—141no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—42no—
658C22×C4—142no—
659C22×C4—142no—
660C22×C4—142no—
661C22×C4C2×C22⋊D711yescharacteristic
662C22×C4C2×C22⋊D711yescharacteristic
663C22×C4C2×C22⋊D711yescharacteristic
664C22×C4C2×C22⋊D711yescharacteristic
665C22×C4C2×C22⋊D711yescharacteristic
666C22×C4C2×C22⋊D711yescharacteristic
667C22×C4C2×C22⋊D711yescharacteristic
668C22×C4C2×C22⋊D711yescharacteristic
669C22×C4C2×C22⋊D711yescharacteristic
670C22×C4C2×C22⋊D711yescharacteristic
671C22×C4C2×C22⋊D711yescharacteristic
672C22×C4C2×C22⋊D711yescharacteristic
673C22×C4C2×C22⋊D711yescharacteristic
674C22×C4C2×C22⋊D711yescharacteristic
675C22×C4C2×C22⋊D711yescharacteristic
676C22×C4C23×D711yescharacteristic
677C22×C4C23×D711yescharacteristic
678C22×C4C23×D711yescharacteristic
679Q16—1416no—
680SD16—1416no—
681M16—78no—
682M16—148no—
683M16—144no—
684C2×C8—74no—
685C2×C8—74no—
686C2×C8—148no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—24no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—22no—
698C4⋊C4—72no—
699C4⋊C4—72no—
700C4⋊C4—142no—
701C4⋊C4—142no—
702C4⋊C4—142no—
703C4⋊C4—142no—
704C4⋊C4—142no—
705C4⋊C4—142no—
706C4⋊C4—141no—
707C4⋊C4—141no—
708C4⋊C4—141no—
709C4⋊C4—141no—
710C4⋊C4C23×D714yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—142no—
714C22⋊C4—142no—
715C22⋊C4—142no—
716C22⋊C4—142no—
717C22⋊C4—142no—
718C22⋊C4—142no—
719C22⋊C4—142no—
720C22⋊C4—142no—
721C22⋊C4—142no—
722C42—24no—
723C42—24no—
724C42—142no—
725C42—142no—
726C42—142no—
727C42C2×C22⋊D711yescharacteristic
728C42C2×C22⋊D711yescharacteristic
729C42C2×C22⋊D711yescharacteristic
730C42C2×C22⋊D711yescharacteristic
731C42C2×C22⋊D711yescharacteristic
732C42C2×C22⋊D711yescharacteristic
733C42C2×C22⋊D711yescharacteristic
734C42C2×C22⋊D711yescharacteristic
735C42C2×C22⋊D711yescharacteristic
736C42C2×C22⋊D711yescharacteristic
737C42C2×C22⋊D711yescharacteristic
738C42C2×C22⋊D711yescharacteristic
739C42C23×D711yescharacteristic
740C42C23×D711yescharacteristic
741C42C23×D711yescharacteristic
742C42C23×D711yescharacteristic
743C2×C7—22no—
744C2×C7—22no—
745C2×C7—41no—
746C2×C7C2×#53211yescharacteristic
747C2×C7C22×#13711yescharacteristic
748C2×C7C2×#57511yescharacteristic
749D7—82no—
750C23—22no—
751C23—22no—
752C23—41no—
753C23—142no—
754C23C22×C22⋊D711yescharacteristic
755C23C22×C22⋊D711yescharacteristic
756C23C22×C22⋊D711yescharacteristic
757Q8—28no—
758Q8—44no—
759Q8—44no—
760Q8—44no—
761Q8—144no—
762Q8—282no—
763Q8—282no—
764D4—144no—
765D4—284no—
766D4—284no—
767D4—284no—
768D4—282no—
769D4—282no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—142no—
791C2×C4—142no—
792C2×C4—142no—
793C2×C4—284no—
794C2×C4—284no—
795C2×C4—284no—
796C2×C4#650514yescomplemented
797C2×C4D7×#4114yes—
798C2×C4C22×C22⋊D711yescharacteristic
799C2×C4C22×C22⋊D711yescharacteristic
800C2×C4C22×C22⋊D711yescharacteristic
801C2×C4C22×C22⋊D711yescharacteristic
802C2×C4C22×C22⋊D711yescharacteristic
803C2×C4C22×C22⋊D711yescharacteristic
804C2×C4C22×C22⋊D711yescharacteristic
805C2×C4C22×C22⋊D711yescharacteristic
806C2×C4C22×C22⋊D711yescharacteristic
807C2×C4C22×C22⋊D711yescharacteristic
808C2×C4C22×C22⋊D711yescharacteristic
809C2×C4C24×D711yescharacteristic
810C8—78no—
811C8—144no—
812C7#6070111yescharacteristic, complemented, Sylow
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—44no—
821C22—282no—
822C22—282no—
823C22—282no—
824C22C2×#650512yes—
825C22#9052312yes—
826C22C23×C22⋊D711yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—44no—
835C4—44no—
836C4—282no—
837C4—282no—
838C4—282no—
839C4C2×#650512yes—
840C4C2×#650512yes—
841C4#9051312yes—
842C4#9052312yes—
843C4C2×D7×#4112yes—
844C2—22no—
845C2—22no—
846C2—41no—
847C2—562no—
848C2C22×#650511yescharacteristic
849C2C2×#9051311yescharacteristic
850C2C2×#9052311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#533C2
socleC22×C7C23×D4
prime radical#11742748C2
hypercenterC2×#533D7
hypocenterC7#60701
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C7×#533C2semidirect
3. #11740793C2semidirect
4. #11740792C2semidirect
5. #11740791C2semidirect
6. #11740790C2semidirect
7. #11740789C2semidirect
8. #11740788C2semidirect
9. #11740652C2semidirect
10. #11740648C2semidirect
11. #11740644C2semidirect
12. #11740643C2semidirect
13. #11740177C2semidirect
14. C4×#6505C2semidirect
15. C2×C4×#1136C2semidirect
54. #89865C22semidirect
55. #89864C22semidirect
56. #89861C22semidirect
57. #89860C22semidirect
58. #89858C22semidirect
59. #89857C22semidirect
60. #89854C22semidirect
61. #89853C22semidirect
62. #89853C22semidirect
63. #89852C22semidirect
64. #89851C22semidirect
65. #89850C22semidirect
70. #89802C22semidirect
71. C4×#1144C22semidirect
72. #89798C22semidirect
73. C4×#1143C22semidirect
218. C2×#533D7semidirect
337. #1136#41semidirect
439. C2×C4×C7#137semidirect
796. C2×C4#6505semidirect
812. C7#60701semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5332
#117427482
#117407932
#117407922
#117407912
#117407902
#117407892
#117407882
#117406522
#117406482
#117406442
#117406432
#117401772
C4×#65052
C2×C4×#11362
#607017