Finite Group Databasebeta

← C2×#11736571 #14232339

Subgroups — C2×#11736571 #14232339

Order 1792.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90202C211yesmaximal, characteristic
2C2×#90204C211yesmaximal, characteristic
3C22×C7×#106C211yesmaximal, characteristic, complemented
4C2×#89888C211yesmaximal, characteristic, complemented
5C2×#89883C211yesmaximal, characteristic
6C2×#89742C211yesmaximal, characteristic, complemented
7C2×#89743C211yesmaximal, characteristic, complemented
8C2×#89629C211yesmaximal, characteristic, complemented
9C2×#89626C211yesmaximal, characteristic, complemented
10#11736571C2116yesmaximal, direct product factor
11C2×#89634C211yesmaximal, characteristic, complemented
12C2×#89640C211yesmaximal, characteristic, complemented
13C2×#89633C211yesmaximal, characteristic, complemented
14C2×#89639C211yesmaximal, characteristic, complemented
15C2×#89628C211yesmaximal, characteristic, complemented
16C2×#89625C211yesmaximal, characteristic, complemented
17C23×C7×C8C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C2×#6492—21no—
21C2×C4×C22⋊D7—21no—
22C2×C4×C22⋊D7C2211yescharacteristic
23C2×#6489—21no—
24C2×#6487—21no—
25C2×#6487C2211yescharacteristic
26C2×#6487C2211yescharacteristic
27C22×Dic28C2211yescharacteristic
28C22×#1131C2211yescharacteristic
29#90204—24no—
30#90204C2218yes—
31C2×#6461—21no—
32#90202—24no—
33#90202C2218yes—
34C2×#6460C2211yescharacteristic
35C2×#6460C2211yescharacteristic
36C2×#6459—21no—
37C2×#6455C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×#6453C2211yescharacteristic
40C2×#6452—21no—
41C2×#6452—21no—
42C2×#6451C2211yescharacteristic
43C2×#6450C2211yescharacteristic
44C2×#6450C2211yescharacteristic
45C2×C7×#106C2211yescharacteristic
46C2×C7×#106C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#106C2218yescomplemented
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51#89888C2218yescomplemented
52#89883C2218yes—
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×#6392C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6389C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59#89743C2218yescomplemented
60#89742C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6381C2211yescharacteristic
69#89640C2218yescomplemented
70#89639C2218yescomplemented
71#89634C2218yescomplemented
72#89633C2218yescomplemented
73#89629C2218yescomplemented
74#89628C2218yescomplemented
75#89626C2218yescomplemented
76#89625C2218yescomplemented
77C2×#3344—71nomaximal, Sylow
78C23×C4×C7—21no—
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7D411yescharacteristic
82C22×C4×D7—21no—
83C22×C4×D7C2311yescharacteristic
84C22×Dic14—21no—
85C22×Dic14C2311yescharacteristic
86C22×Dic14C2311yescharacteristic
87C22×C7×C8—24no—
88C22×C7×C8C2311yescharacteristic
89C22×C7×C8C2314yes—
90C22×C7×C8C2311yescharacteristic
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4—21no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4C2311yescharacteristic
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2314yes—
100C2×C7×C4⋊C4C2314yes—
101C2×C22⋊Dic7—21no—
102C2×C22⋊Dic7—21no—
103C2×C22⋊Dic7D411yescharacteristic
104#6492—28no—
105C4×C22⋊D7—28no—
106C4×C22⋊D7D414yes—
107C4×C22⋊D7C2314yes—
108C2×(C2×D7)⋊C4—21no—
109C2×(C2×D7)⋊C4—21no—
110C2×(C2×D7)⋊C4—21no—
111C2×(C2×D7)⋊C4D411yescharacteristic
112#6489—28no—
113C2×C4⋊Dic7—21no—
114C2×C4⋊Dic7—21no—
115C2×C4⋊Dic7—21no—
116C2×C4⋊Dic7C2311yescharacteristic
117C2×C4⋊Dic7C2311yescharacteristic
118#6487—22no—
119#6487—22no—
120#6487—28no—
121#6487C2314yes—
122#6487C2314yes—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4D411yescharacteristic
131C2×C4×Dic7—21no—
132C2×C4×Dic7—21no—
133C2×C4×Dic7—21no—
134C2×C4×Dic7C2311yescharacteristic
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C2×Dic28—24no—
138C2×Dic28C2314yes—
139C2×#1131—24no—
140C2×#1131C2314yes—
141#6461—28no—
142#6460—22no—
143#6460—22no—
144#6460C2314yes—
145#6460C2314yes—
146#6459—28no—
147#6455—22no—
148#6455C2314yes—
149D7×C4⋊C4—22no—
150D7×C4⋊C4C2314yes—
151#6453—22no—
152#6453C2314yes—
153#6452—28no—
154#6452—28no—
155#6451—22no—
156#6451C2314yes—
157#6450—22no—
158#6450—22no—
159#6450C2314yes—
160#6450C2314yes—
161C7×#106C2314yes—
162C7×#106C2314yes—
163C7×#106C2314yes—
164C7×#106C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166(C2×D7)⋊C8C2314yes—
167#6392C2314yes—
168#6390C2314yes—
169#6390C2314yes—
170#6389C2314yes—
171Dic7⋊C8C2314yes—
172#6384C2314yes—
173#6384C2314yes—
174#6384C2314yes—
175#6384C2314yes—
176#6382C2314yes—
177#6382C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180C2×#554—71no—
181C2×#552—71no—
182#3344—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#485—71no—
186C2×#483—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#475—71no—
190C2×#470—71no—
191C2×#467—71no—
192C2×#441—71no—
193C2×#435—71no—
194C2×#428—71no—
195C22×#106D711yescharacteristic, complemented
196C24×C7C2×D411yescharacteristic
197C23×D7C2×D411yescharacteristic
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—24no—
205C22×C4×C7—24no—
206C22×C4×C7—44no—
207C22×C4×C7—82no—
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D412yes—
210C22×C4×C7C2412yes—
211C22×C4×C7C2411yescharacteristic
212C2×C22⋊D7—24no—
213C2×C22⋊D7C2×D414yes—
214C22×Dic7—21no—
215C22×Dic7—21no—
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7C2×D411yescharacteristic
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C2×C4×D7—22no—
222C2×C4×D7—22no—
223C2×C4×D7—24no—
224C2×C4×D7—82no—
225C2×C4×D7C2×D412yes—
226C2×C4×D7C2412yes—
227C2×Dic14—22no—
228C2×Dic14—22no—
229C2×Dic14—22no—
230C2×Dic14—22no—
231C2×Dic14—21no—
232C2×Dic14—21no—
233C2×Dic14—24no—
234C2×Dic14—82no—
235C2×Dic14C2412yes—
236C2×Dic14C2412yes—
237C2×C7×C8—22no—
238C2×C7×C8—28no—
239C2×C7×C8#4114yes—
240C2×C7×C8C2412yes—
241C2×C7×C8C2412yes—
242C7×C4⋊C4—21no—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—21no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4C2412yes—
249C7×C4⋊C4C2412yes—
250C7×C4⋊C4C2412yes—
251C7×C4⋊C4C2412yes—
252C22⋊Dic7—24no—
253C22⋊Dic7—24no—
254C22⋊Dic7C2×D414yes—
255(C2×D7)⋊C4—24no—
256(C2×D7)⋊C4—24no—
257(C2×D7)⋊C4—24no—
258(C2×D7)⋊C4C2×D414yes—
259C4⋊Dic7—21no—
260C4⋊Dic7—21no—
261C4⋊Dic7—24no—
262C4⋊Dic7—24no—
263C4⋊Dic7—24no—
264C4⋊Dic7C2412yes—
265C4⋊Dic7C2412yes—
266Dic7⋊C4—24no—
267Dic7⋊C4—24no—
268Dic7⋊C4—24no—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4C2×D414yes—
274C4×Dic7—24no—
275C4×Dic7—24no—
276C4×Dic7—24no—
277C4×Dic7C2×D412yes—
278C4×Dic7C2412yes—
279C2×C7⋊C8—22no—
280C2×C7⋊C8—22no—
281C2×C7⋊C8C2412yes—
282C2×C7⋊C8C2412yes—
283Dic28—28no—
284#1131—28no—
285C22×Q16—71no—
286C22×M16—71no—
287C23×C8C2×D711yescharacteristic
288#554—78no—
289#554—144no—
290#552—78no—
291#552—144no—
292C2×C4⋊Q8—71no—
293C2×#126—141no—
294C2×#125—71no—
295C2×#125—141no—
296C2×#125—141no—
297C2×#123—141no—
298C2×C22⋊Q8—71no—
299C2×C22⋊Q8—71no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×C4×Q8—71no—
305C2×C4×Q8—71no—
306C2×C4×D4—71no—
307C2×C4×D4—141no—
308C2×#117—71no—
309C2×#117—141no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4C2×D711yescharacteristic
312C22×C4⋊C4C2×D711yescharacteristic
313#501—78no—
314#485—78no—
315#484—78no—
316#483—78no—
317#483—78no—
318#479—78no—
319#475—78no—
320#470—78no—
321#467—78no—
322#441—78no—
323#435—78no—
324#428—78no—
325C2×#107—71no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×#106C2×D711yescharacteristic
331C2×#106C2×D711yescharacteristic
332C2×#106C2×D711yescharacteristic
333C2×#106C2×D711yescharacteristic
334C2×#106C2×D718yescomplemented
335C2×C4⋊C8—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#103—71no—
341C2×#103—71no—
342C2×C22⋊C8—71no—
343C2×C22⋊C8—71no—
344C2×#97—71no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7#13714yes—
348C23×C7C22×D412yes—
349C23×C7C22×D411yescharacteristic
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7C22×D412yes—
354C2×C4×C7—22no—
355C2×C4×C7—24no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—48no—
363C2×C4×C7—42no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—84no—
368C2×C4×C7C22×D412yes—
369C2×C4×C7C22×D411yescharacteristic
370C2×C4×C7C2×#4112yes—
371C2×C4×C72−1+412yes—
372C2×C4×C7C2511yescharacteristic
373C22⋊D7—28no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—42no—
382C2×Dic7—42no—
383C2×Dic7—42no—
384C2×Dic7—42no—
385C2×Dic7C22×D412yes—
386C2×Dic7C22×D412yes—
387C2×Dic7C22×D412yes—
388C4×D7—24no—
389C4×D7—22no—
390C4×D7—22no—
391C4×D7—84no—
392Dic14—22no—
393Dic14—22no—
394Dic14—22no—
395Dic14—22no—
396Dic14—42no—
397Dic14—42no—
398Dic14—84no—
399C7×C8—22no—
400C7×C8C2×#4114yes—
401C7⋊C8—22no—
402C7⋊C8—22no—
403C22×Q8—71no—
404C22×Q8—71no—
405C22×Q8—141no—
406C22×D4—71no—
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—71no—
410C23×C4—141no—
411C23×C4C22×D711yescharacteristic
412C2×Q16—74no—
413C2×Q16—144no—
414C2×M16—74no—
415C2×M16—144no—
416C22×C8—24no—
417C22×C8—71no—
418C22×C8—71no—
419C22×C8C22×D711yescharacteristic
420C22×C8C22×D714yes—
421C22×C8C22×D711yescharacteristic
422C4⋊Q8—74no—
423C4⋊Q8—142no—
424#126—148no—
425#125—74no—
426#125—142no—
427#125—148no—
428#125—148no—
429#123—148no—
430C22⋊Q8—74no—
431C22⋊Q8—74no—
432C22⋊Q8—74no—
433C22⋊Q8—74no—
434C22⋊Q8—148no—
435C22⋊Q8—148no—
436C22⋊Q8—142no—
437C22⋊Q8—142no—
438C22⋊Q8—142no—
439C22⋊Q8—142no—
440C4×Q8—74no—
441C4×Q8—74no—
442C4×Q8—142no—
443C4×Q8—142no—
444C4×D4—74no—
445C4×D4—74no—
446C4×D4—148no—
447#117—74no—
448#117—148no—
449#117—142no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—71no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—71no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—142no—
459C2×C4⋊C4—141no—
460C2×C4⋊C4—141no—
461C2×C4⋊C4—141no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4—141no—
464C2×C4⋊C4—141no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4C22×D711yescharacteristic
470C2×C4⋊C4C22×D711yescharacteristic
471C2×C4⋊C4C22×D711yescharacteristic
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D714yes—
474C2×C4⋊C4C22×D714yes—
475C2×C22⋊C4—71no—
476C2×C22⋊C4—71no—
477C2×C22⋊C4—141no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C42—71no—
483C2×C42—141no—
484C2×C42—141no—
485C2×C42—141no—
486#107—74no—
487#107—74no—
488#107—74no—
489#106—74no—
490#106—74no—
491#106C22×D714yes—
492#106C22×D714yes—
493#106C22×D714yes—
494#106C22×D714yes—
495C4⋊C8—74no—
496#103—74no—
497#103—74no—
498#103—74no—
499#103—74no—
500#103—74no—
501#103—74no—
502C22⋊C8—74no—
503C22⋊C8—74no—
504#97—74no—
505C22×C7—28no—
506C22×C7—22no—
507C22×C7—22no—
508C22×C7#54712yes—
509C22×C7C2×#13714yes—
510C22×C7C2×#13712yes—
511C22×C7#57712yes—
512C22×C7C23×D411yescharacteristic
513C2×D7—22no—
514C2×D7—22no—
515C2×D7—22no—
516C2×D7—44no—
517C4×C7—22no—
518C4×C7—42no—
519C4×C7—42no—
520C4×C7—42no—
521C4×C7—42no—
522C4×C7#54712yes—
523C4×C7C22×#4111yescharacteristic
524C4×C7C2×2−1+411yescharacteristic
525Dic7—22no—
526Dic7—22no—
527Dic7—22no—
528Dic7—42no—
529Dic7—42no—
530Dic7—42no—
531Dic7—42no—
532C24—71no—
533C24D4×D711yescharacteristic
534C2×Q8—72no—
535C2×Q8—72no—
536C2×Q8—144no—
537C2×Q8—141no—
538C2×Q8—141no—
539C2×Q8—142no—
540C2×Q8—142no—
541C2×Q8—142no—
542C2×Q8—142no—
543C2×Q8—562no—
544C2×D4—74no—
545C2×D4—144no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—44no—
555C22×C4—71no—
556C22×C4—71no—
557C22×C4—71no—
558C22×C4—72no—
559C22×C4—72no—
560C22×C4—82no—
561C22×C4—144no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—141no—
568C22×C4—562no—
569C22×C4D4×D712yes—
570C22×C4D4×D711yescharacteristic
571C22×C4C23×D712yes—
572C22×C4C23×D711yescharacteristic
573Q16—148no—
574M16—148no—
575C2×C8—22no—
576C2×C8—28no—
577C2×C8—72no—
578C2×C8—72no—
579C2×C8—142no—
580C2×C8—142no—
581C2×C8#115714yes—
582C2×C8C23×D712yes—
583C2×C8C23×D712yes—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—24no—
590C4⋊C4—74no—
591C4⋊C4—72no—
592C4⋊C4—72no—
593C4⋊C4—144no—
594C4⋊C4—144no—
595C4⋊C4—144no—
596C4⋊C4—144no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—144no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—141no—
604C4⋊C4—141no—
605C4⋊C4C23×D712yes—
606C4⋊C4C23×D712yes—
607C4⋊C4C23×D712yes—
608C4⋊C4C23×D712yes—
609C22⋊C4—74no—
610C22⋊C4—74no—
611C22⋊C4—144no—
612C22⋊C4—144no—
613C22⋊C4—144no—
614C22⋊C4—144no—
615C22⋊C4—144no—
616C42—72no—
617C42—72no—
618C42—144no—
619C42—144no—
620C42—144no—
621C2×C7—24no—
622C2×C7#334414yescomplemented
623C2×C7C2×#54711yescharacteristic
624C2×C7C22×#13711yescharacteristic
625C2×C7C2×#57711yescharacteristic
626D7—42no—
627C23—22no—
628C23—22no—
629C23—72no—
630C23—142no—
631C23—142no—
632C23—142no—
633C23#647814yes—
634C23C2×D4×D712yes—
635C23C2×D4×D711yescharacteristic
636Q8—142no—
637Q8—142no—
638Q8—142no—
639Q8—142no—
640Q8—282no—
641Q8—282no—
642Q8—564no—
643D4—148no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—72no—
658C2×C4—72no—
659C2×C4—72no—
660C2×C4—84no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—144no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—142no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—282no—
674C2×C4—282no—
675C2×C4—564no—
676C2×C4C2×#115712yes—
677C2×C4C2×D4×D712yes—
678C2×C4C2×D4×D711yescharacteristic
679C2×C4#655112yes—
680C2×C4C24×D711yescharacteristic
681C8—22no—
682C8—142no—
683C8—142no—
684C8C2×#115714yes—
685C7C2×#334411yescharacteristic, complemented, Sylow
686C22—22no—
687C22—22no—
688C22—28no—
689C22—142no—
690C22—142no—
691C22—142no—
692C22—284no—
693C22#9019812yes—
694C22C2×#647814yes—
695C22C2×#647812yes—
696C22#9045312yes—
697C22C22×D4×D711yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—142no—
704C4—142no—
705C4—142no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C4#9019812yes—
711C4C22×#115711yescharacteristic
712C4C2×#655111yescharacteristic
713C2—24no—
714C2—282no—
715C2#1173657114yesdirect product factor
716C2C2×#9019811yescharacteristic
717C2C22×#647811yescharacteristic
718C2C2×#9045311yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC22×C7×#106C2
socleC23×C7C22×D4
prime radicalC22×C22⋊D7D4
hypercenterC22×#106D7
hypocenterC7C2×#3344
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. C22×C7×#106C2semidirect
4. C2×#89888C2semidirect
6. C2×#89742C2semidirect
7. C2×#89743C2semidirect
8. C2×#89629C2semidirect
9. C2×#89626C2semidirect
10. #11736571C2direct (N × H)
11. C2×#89634C2semidirect
12. C2×#89640C2semidirect
13. C2×#89633C2semidirect
14. C2×#89639C2semidirect
15. C2×#89628C2semidirect
16. C2×#89625C2semidirect
49. C2×C7×#106C22semidirect
51. #89888C22semidirect
59. #89743C22semidirect
60. #89742C22semidirect
69. #89640C22semidirect
70. #89639C22semidirect
71. #89634C22semidirect
72. #89633C22semidirect
73. #89629C22semidirect
74. #89628C22semidirect
75. #89626C22semidirect
76. #89625C22semidirect
195. C22×#106D7semidirect
334. C2×#106C2×D7semidirect
622. C2×C7#3344semidirect
685. C7C2×#3344semidirect
715. C2#11736571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902022
C2×#902042
C22×C7×#1062
C2×#898882
C2×#898832
C2×#897422
C2×#897432
C2×#896292
C2×#896262
#117365712
C2×#896342
C2×#896402
C2×#896332
C2×#896392
C2×#896282
C2×#896252
C2×#33447